| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2492.001120$ |
0.366877209 |
\( -\frac{12495}{2} a^{3} + \frac{4709}{2} a^{2} + \frac{77707}{2} a + 29265 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -5 a^{3} - a^{2} + 24 a + 18\) , \( -\frac{15}{2} a^{3} - \frac{3}{2} a^{2} + \frac{71}{2} a + 26\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+4\right){x}^{2}+\left(-5a^{3}-a^{2}+24a+18\right){x}-\frac{15}{2}a^{3}-\frac{3}{2}a^{2}+\frac{71}{2}a+26$ |
| 1.1-a2 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$623.0002802$ |
0.366877209 |
\( -\frac{956891123}{2} a^{3} + \frac{184745949}{2} a^{2} + \frac{5456330747}{2} a + 1913979664 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -\frac{15}{2} a^{3} - \frac{7}{2} a^{2} + \frac{53}{2} a + 18\) , \( -15 a^{3} - 15 a^{2} + 41 a + 36\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+4\right){x}^{2}+\left(-\frac{15}{2}a^{3}-\frac{7}{2}a^{2}+\frac{53}{2}a+18\right){x}-15a^{3}-15a^{2}+41a+36$ |
| 1.1-a3 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$30.76544593$ |
0.366877209 |
\( \frac{11454772099655}{2} a^{3} + \frac{16476545963211}{2} a^{2} - \frac{17103076638427}{2} a - 9396387712126 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -\frac{35}{2} a^{3} - \frac{47}{2} a^{2} + \frac{93}{2} a + 38\) , \( -99 a^{3} - 141 a^{2} + 175 a + 174\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+4\right){x}^{2}+\left(-\frac{35}{2}a^{3}-\frac{47}{2}a^{2}+\frac{93}{2}a+38\right){x}-99a^{3}-141a^{2}+175a+174$ |
| 1.1-a4 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$30.76544593$ |
0.366877209 |
\( \frac{34051050961357}{2} a^{3} - \frac{61982369024223}{2} a^{2} - \frac{119414392544609}{2} a + 83028186306741 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 14 a^{3} + 9 a^{2} - 71 a - 88\) , \( \frac{245}{2} a^{3} + \frac{93}{2} a^{2} - \frac{1209}{2} a - 580\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(14a^{3}+9a^{2}-71a-88\right){x}+\frac{245}{2}a^{3}+\frac{93}{2}a^{2}-\frac{1209}{2}a-580$ |
| 1.1-a5 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$623.0002802$ |
0.366877209 |
\( -\frac{50135021}{2} a^{3} + \frac{822280195}{2} a^{2} - \frac{2435252315}{2} a + 890372831 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{3} - 6 a^{2} + 14 a + 12\) , \( -\frac{17}{2} a^{3} + \frac{23}{2} a^{2} + \frac{49}{2} a - 6\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(-a^{3}-6a^{2}+14a+12\right){x}-\frac{17}{2}a^{3}+\frac{23}{2}a^{2}+\frac{49}{2}a-6$ |
| 1.1-a6 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$623.0002802$ |
0.366877209 |
\( -\frac{406047}{2} a^{3} - \frac{56087}{2} a^{2} + \frac{1966631}{2} a + 713389 \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - \frac{9}{2} a - 4\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}+\frac{3}{2}a^{3}+\frac{3}{2}a^{2}-\frac{9}{2}a-4$ |
| 1.1-a7 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2492.001120$ |
0.366877209 |
\( \frac{3723}{2} a^{3} + \frac{4063}{2} a^{2} - \frac{51391}{2} a + 26018 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{2} + 2 a + 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( -3 a^{3} + a^{2} + 14 a + 7\) , \( -3 a^{3} + a^{2} + 14 a + 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-3a^{3}+a^{2}+14a+7\right){x}-3a^{3}+a^{2}+14a+5$ |
| 1.1-a8 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.691361484$ |
0.366877209 |
\( \frac{3464946905534287422448807585}{2} a^{3} - \frac{6307067008351224343169529695}{2} a^{2} - \frac{12151367540253075049485032893}{2} a + 8448521965185185103366369798 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{3} - 72 a^{2} - 205 a - 123\) , \( -14 a^{3} - 662 a^{2} - 1638 a - 908\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){x}^{2}+\left(a^{3}-72a^{2}-205a-123\right){x}-14a^{3}-662a^{2}-1638a-908$ |
| 1.1-a9 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.691361484$ |
0.366877209 |
\( -\frac{908842487857362269}{2} a^{3} - \frac{125933091424244925}{2} a^{2} + \frac{4400829521584278145}{2} a + 1596471127189922426 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -a^{2} + a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -5 a - 5\) , \( 19 a^{3} - 51 a^{2} - 16 a + 31\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-5a-5\right){x}+19a^{3}-51a^{2}-16a+31$ |
| 1.1-a10 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.691361484$ |
0.366877209 |
\( -\frac{589079248492070197}{2} a^{3} + \frac{1623854827773677391}{2} a^{2} + \frac{92935687464019253}{2} a - 670704581648803487 \) |
\( \bigl[a + 1\) , \( -a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -3 a^{3} + 2 a^{2} + 14 a - 7\) , \( \frac{47}{2} a^{3} + \frac{19}{2} a^{2} - \frac{227}{2} a - 122\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}-a{x}^{2}+\left(-3a^{3}+2a^{2}+14a-7\right){x}+\frac{47}{2}a^{3}+\frac{19}{2}a^{2}-\frac{227}{2}a-122$ |
| 1.1-a11 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$623.0002802$ |
0.366877209 |
\( -\frac{262869}{2} a^{3} + \frac{725003}{2} a^{2} + \frac{40117}{2} a - 298768 \) |
\( \bigl[a + 1\) , \( -a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{5}{2} a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}-a{x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{5}{2}a+3$ |
| 1.1-a12 |
1.1-a |
$12$ |
$24$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$4.21506$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$7.691361484$ |
0.366877209 |
\( \frac{1165623442300712571019141461}{2} a^{3} + \frac{1676496660516224349701580649}{2} a^{2} - \frac{1740343503251924930918814245}{2} a - 956101755090732049865101601 \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 4\) , \( a\) , \( -\frac{267}{2} a^{3} + \frac{411}{2} a^{2} + \frac{1199}{2} a - 751\) , \( -1496 a^{3} + 2444 a^{2} + 6239 a - 8064\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(-\frac{267}{2}a^{3}+\frac{411}{2}a^{2}+\frac{1199}{2}a-751\right){x}-1496a^{3}+2444a^{2}+6239a-8064$ |
| 16.1-a1 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.145659266$ |
1.125565163 |
\( -\frac{21417711216510281745097895}{64} a^{3} - \frac{370966176885404047689177}{8} a^{2} + \frac{6481850338880742243324709}{4} a + 1175697316394585477461175 \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( a^{2} - a - 2\) , \( -63 a^{3} - 511 a^{2} - 334 a - 99\) , \( -\frac{7331}{2} a^{3} - \frac{23441}{2} a^{2} - \frac{5689}{2} a + 2767\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(-63a^{3}-511a^{2}-334a-99\right){x}-\frac{7331}{2}a^{3}-\frac{23441}{2}a^{2}-\frac{5689}{2}a+2767$ |
| 16.1-a2 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$11.79840057$ |
1.125565163 |
\( -\frac{4805055317535}{262144} a^{3} - \frac{83328303025}{32768} a^{2} + \frac{1454285809955}{16384} a + \frac{2110395388989}{32768} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{3}{2} a + 4\) , \( a^{2} - a - 2\) , \( -3 a^{3} - 11 a^{2} + 6 a + 21\) , \( \frac{13}{2} a^{3} - \frac{17}{2} a^{2} - \frac{57}{2} a - 9\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{3}{2}a+4\right){x}^{2}+\left(-3a^{3}-11a^{2}+6a+21\right){x}+\frac{13}{2}a^{3}-\frac{17}{2}a^{2}-\frac{57}{2}a-9$ |
| 16.1-a3 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$955.6704461$ |
1.125565163 |
\( \frac{546880529}{128} a^{3} - \frac{995601459}{128} a^{2} - \frac{1917966475}{128} a + \frac{666851395}{32} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{3}+2a^{2}+4a-4\right){x}+a^{3}-2a^{2}-3a+7$ |
| 16.1-a4 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$955.6704461$ |
1.125565163 |
\( \frac{45964405}{32} a^{3} + \frac{132431655}{64} a^{2} - \frac{68561993}{32} a - \frac{37780611}{16} \) |
\( \bigl[a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + 1\) , \( a^{2} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+1\right){x}^{2}+\left(a^{2}-2a\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+1$ |
| 16.1-a5 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$81$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.145659266$ |
1.125565163 |
\( -\frac{13882195646026523479452721}{64} a^{3} + \frac{1195863633675626175189501}{2} a^{2} + \frac{273764395689817472557063}{8} a - \frac{31611543767746583544251007}{64} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -610 a^{3} + 1181 a^{2} + 2357 a - 4063\) , \( -\frac{39313}{2} a^{3} + \frac{73397}{2} a^{2} + \frac{143695}{2} a - 109064\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+2\right){x}^{2}+\left(-610a^{3}+1181a^{2}+2357a-4063\right){x}-\frac{39313}{2}a^{3}+\frac{73397}{2}a^{2}+\frac{143695}{2}a-109064$ |
| 16.1-a6 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$11.79840057$ |
1.125565163 |
\( -\frac{3114192685065}{262144} a^{3} + \frac{536617151675}{16384} a^{2} + \frac{61146381065}{32768} a - \frac{7093520331823}{262144} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -10 a^{3} + 21 a^{2} + 37 a - 63\) , \( -\frac{33}{2} a^{3} + \frac{69}{2} a^{2} + \frac{111}{2} a - 104\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+2\right){x}^{2}+\left(-10a^{3}+21a^{2}+37a-63\right){x}-\frac{33}{2}a^{3}+\frac{69}{2}a^{2}+\frac{111}{2}a-104$ |
| 16.1-b1 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{50} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$2.751400638$ |
0.729119711 |
\( \frac{888291634749271321}{2097152} a^{3} - \frac{1616912130457070213}{2097152} a^{2} - \frac{3115187239876266733}{2097152} a + \frac{2165906537306684017}{1048576} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 1\) , \( 0\) , \( -\frac{91}{2} a^{3} - \frac{131}{2} a^{2} + \frac{145}{2} a + 64\) , \( -\frac{1923}{2} a^{3} - \frac{2783}{2} a^{2} + \frac{2849}{2} a + 1546\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}={x}^{3}+{x}^{2}+\left(-\frac{91}{2}a^{3}-\frac{131}{2}a^{2}+\frac{145}{2}a+64\right){x}-\frac{1923}{2}a^{3}-\frac{2783}{2}a^{2}+\frac{2849}{2}a+1546$ |
| 16.1-b2 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{50} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2 \) |
$1$ |
$2.751400638$ |
0.729119711 |
\( \frac{149412609540572745}{1048576} a^{3} + \frac{214897638313326701}{1048576} a^{2} - \frac{111540830403745925}{524288} a - \frac{61277779407734761}{262144} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 7 a^{3} + 11 a^{2} - 12 a - 132\) , \( -\frac{31}{2} a^{3} + \frac{449}{2} a^{2} + \frac{27}{2} a - 1143\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(7a^{3}+11a^{2}-12a-132\right){x}-\frac{31}{2}a^{3}+\frac{449}{2}a^{2}+\frac{27}{2}a-1143$ |
| 16.1-b3 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$100$ |
\( 1 \) |
$1$ |
$1.375700319$ |
0.729119711 |
\( -\frac{385603532444261137105}{64} a^{3} + \frac{385603532444261137105}{64} a^{2} + \frac{1156810597332783411315}{64} a + \frac{238316089232576270321}{32} \) |
\( \bigl[a^{2} - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - 3\) , \( a^{2} - 3\) , \( \frac{1373}{2} a^{3} - \frac{4061}{2} a^{2} + \frac{341}{2} a + 1401\) , \( \frac{57843}{2} a^{3} - \frac{160487}{2} a^{2} - \frac{7077}{2} a + 65326\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(\frac{1373}{2}a^{3}-\frac{4061}{2}a^{2}+\frac{341}{2}a+1401\right){x}+\frac{57843}{2}a^{3}-\frac{160487}{2}a^{2}-\frac{7077}{2}a+65326$ |
| 16.1-b4 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$1719.625399$ |
0.729119711 |
\( -\frac{50109851}{8} a^{3} - \frac{13881241}{16} a^{2} + \frac{242645051}{8} a + \frac{88020739}{4} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{3} - 4 a^{2} - 3 a + 2\) , \( \frac{7}{2} a^{3} + \frac{9}{2} a^{2} - \frac{11}{2} a - 5\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{3}-4a^{2}-3a+2\right){x}+\frac{7}{2}a^{3}+\frac{9}{2}a^{2}-\frac{11}{2}a-5$ |
| 16.1-b5 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$4$ |
\( 1 \) |
$1$ |
$859.8126995$ |
0.729119711 |
\( \frac{908026183625}{4} a^{3} - \frac{908026183625}{4} a^{2} - \frac{2724078550875}{4} a + 734608622353 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{1}{2} a - 2\) , \( a^{2} - 3\) , \( -a^{3} - 9 a^{2} + 22 a - 12\) , \( \frac{141}{2} a^{3} - \frac{347}{2} a^{2} - \frac{121}{2} a + 189\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{1}{2}a-2\right){x}^{2}+\left(-a^{3}-9a^{2}+22a-12\right){x}+\frac{141}{2}a^{3}-\frac{347}{2}a^{2}-\frac{121}{2}a+189$ |
| 16.1-b6 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{40} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$5.502801277$ |
0.729119711 |
\( -\frac{2376401567779}{2048} a^{3} + \frac{2376401567779}{2048} a^{2} + \frac{7129204703337}{2048} a + \frac{735163478721}{512} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{2} - 2\) , \( 507 a^{3} + 75 a^{2} - 2471 a - 1833\) , \( 11504 a^{3} + 1595 a^{2} - 55760 a - 40525\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-4\right){x}^{2}+\left(507a^{3}+75a^{2}-2471a-1833\right){x}+11504a^{3}+1595a^{2}-55760a-40525$ |
| 16.1-b7 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$3439.250798$ |
0.729119711 |
\( \frac{1790195}{8} a^{3} - \frac{1790195}{8} a^{2} - \frac{5370585}{8} a + \frac{2926869}{4} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{2} - 2\) , \( 2 a^{3} - 11 a - 8\) , \( -10 a^{3} - 2 a^{2} + 48 a + 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-4\right){x}^{2}+\left(2a^{3}-11a-8\right){x}-10a^{3}-2a^{2}+48a+36$ |
| 16.1-b8 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$1719.625399$ |
0.729119711 |
\( -\frac{129909351}{32} a^{3} + \frac{358111237}{32} a^{2} + \frac{20466061}{32} a - \frac{73945853}{8} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{3} - 7 a^{2} + 8 a + 6\) , \( -3 a^{3} + 11 a^{2} - 5 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(a^{3}-7a^{2}+8a+6\right){x}-3a^{3}+11a^{2}-5a-10$ |
| 19.1-a1 |
19.1-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$6.09043$ |
$(1/2a^3-3/2a^2-1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$217.4274603$ |
1.152363234 |
\( \frac{1598792626}{19} a^{3} - \frac{2783527522}{19} a^{2} - \frac{5527860549}{19} a + \frac{7542480177}{19} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -3 a^{3} - 3 a^{2} + 5 a + 4\) , \( -16 a^{3} - 23 a^{2} + 25 a + 27\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(-3a^{3}-3a^{2}+5a+4\right){x}-16a^{3}-23a^{2}+25a+27$ |
| 19.1-a2 |
19.1-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{8} \) |
$6.09043$ |
$(1/2a^3-3/2a^2-1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$108.7137301$ |
1.152363234 |
\( \frac{92552153363284660}{16983563041} a^{3} + \frac{66917950344298997}{16983563041} a^{2} - \frac{179110212086206138}{16983563041} a - \frac{19423552243094385}{16983563041} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( 6 a^{3} - 28 a^{2} + 35 a - 9\) , \( -\frac{139}{2} a^{3} + \frac{313}{2} a^{2} + \frac{267}{2} a - 251\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(6a^{3}-28a^{2}+35a-9\right){x}-\frac{139}{2}a^{3}+\frac{313}{2}a^{2}+\frac{267}{2}a-251$ |
| 19.1-a3 |
19.1-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{4} \) |
$6.09043$ |
$(1/2a^3-3/2a^2-1/2a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$434.8549206$ |
1.152363234 |
\( -\frac{6593184883}{130321} a^{3} + \frac{2678496927}{130321} a^{2} + \frac{26352219634}{130321} a + \frac{16630098173}{130321} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -a^{2} + a + 3\) , \( a^{2} - 2\) , \( \frac{17}{2} a^{3} - \frac{51}{2} a^{2} + \frac{5}{2} a + 21\) , \( \frac{67}{2} a^{3} - \frac{189}{2} a^{2} - \frac{3}{2} a + 76\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(\frac{17}{2}a^{3}-\frac{51}{2}a^{2}+\frac{5}{2}a+21\right){x}+\frac{67}{2}a^{3}-\frac{189}{2}a^{2}-\frac{3}{2}a+76$ |
| 19.1-a4 |
19.1-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$6.09043$ |
$(1/2a^3-3/2a^2-1/2a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$434.8549206$ |
1.152363234 |
\( -\frac{379239815884}{361} a^{3} + \frac{1045413444949}{361} a^{2} + \frac{59826090630}{361} a - \frac{863574260399}{361} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 4\) , \( a + 1\) , \( -a^{3} - a^{2} + 6 a + 5\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{15}{2} a - 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+4\right){x}^{2}+\left(-a^{3}-a^{2}+6a+5\right){x}+\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-\frac{15}{2}a-5$ |
| 19.1-a5 |
19.1-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{2} \) |
$6.09043$ |
$(1/2a^3-3/2a^2-1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$108.7137301$ |
1.152363234 |
\( -\frac{4678351774560}{361} a^{3} - \frac{648252464829}{361} a^{2} + \frac{22653681959498}{361} a + \frac{16435969522901}{361} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( 2 a^{2} - 2 a - 3\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{3}{2} a - 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(2a^{2}-2a-3\right){x}+\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{3}{2}a-2$ |
| 19.1-a6 |
19.1-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$6.09043$ |
$(1/2a^3-3/2a^2-1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$54.35686508$ |
1.152363234 |
\( -\frac{238451843945748300466}{19} a^{3} + \frac{657315936650561061710}{19} a^{2} + \frac{37619193173970978989}{19} a - \frac{542985496932508946577}{19} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( a\) , \( 4 a^{3} + a^{2} - 14 a - 8\) , \( -5 a^{3} - 7 a^{2} + 17 a + 23\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}^{2}+\left(4a^{3}+a^{2}-14a-8\right){x}-5a^{3}-7a^{2}+17a+23$ |
| 19.2-a1 |
19.2-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$6.09043$ |
$(1/2a^3-1/2a^2-1/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$217.4274603$ |
1.152363234 |
\( \frac{1281367685}{38} a^{3} + \frac{1088102107}{38} a^{2} - \frac{2381137713}{38} a - \frac{297411870}{19} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 2 a + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{21}{2} a^{3} + \frac{41}{2} a^{2} + \frac{67}{2} a - 50\) , \( -\frac{59}{2} a^{3} + \frac{109}{2} a^{2} + \frac{211}{2} a - 153\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-\frac{21}{2}a^{3}+\frac{41}{2}a^{2}+\frac{67}{2}a-50\right){x}-\frac{59}{2}a^{3}+\frac{109}{2}a^{2}+\frac{211}{2}a-153$ |
| 19.2-a2 |
19.2-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$6.09043$ |
$(1/2a^3-1/2a^2-1/2a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$434.8549206$ |
1.152363234 |
\( -\frac{1170199359725}{722} a^{3} - \frac{162147898405}{722} a^{2} + \frac{5666384793219}{722} a + \frac{2055574156969}{361} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( a^{2} - 2 a - 3\) , \( a\) , \( -a^{2} + 2 a + 1\) , \( a^{3} - 3 a^{2} + 2\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-a^{2}+2a+1\right){x}+a^{3}-3a^{2}+2$ |
| 19.2-a3 |
19.2-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{8} \) |
$6.09043$ |
$(1/2a^3-1/2a^2-1/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$108.7137301$ |
1.152363234 |
\( \frac{443120658437800819}{33967126082} a^{3} - \frac{762060865852968133}{33967126082} a^{2} - \frac{1526454471320698141}{33967126082} a + \frac{1035943318006055399}{16983563041} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( a^{2} - a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( 22 a^{3} - 120 a - 88\) , \( -63 a^{3} - 25 a^{2} + 263 a + 199\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(22a^{3}-120a-88\right){x}-63a^{3}-25a^{2}+263a+199$ |
| 19.2-a4 |
19.2-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{2} \) |
$6.09043$ |
$(1/2a^3-1/2a^2-1/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$108.7137301$ |
1.152363234 |
\( -\frac{6064681152691}{722} a^{3} + \frac{16717889631469}{722} a^{2} + \frac{956790186437}{722} a - \frac{6905029277615}{361} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{7}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( -2 a^{2} + 2 a + 7\) , \( \frac{3}{2} a^{3} - \frac{7}{2} a^{2} - \frac{9}{2} a + 10\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{7}{2}a+2\right){x}^{2}+\left(-2a^{2}+2a+7\right){x}+\frac{3}{2}a^{3}-\frac{7}{2}a^{2}-\frac{9}{2}a+10$ |
| 19.2-a5 |
19.2-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{4} \) |
$6.09043$ |
$(1/2a^3-1/2a^2-1/2a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$434.8549206$ |
1.152363234 |
\( -\frac{10528392737}{260642} a^{3} + \frac{18357768649}{260642} a^{2} + \frac{18439848241}{260642} a - \frac{285364578}{130321} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{15}{2} a - 5\) , \( -\frac{3}{2} a^{3} - \frac{13}{2} a^{2} - \frac{17}{2} a - 3\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{15}{2}a-5\right){x}-\frac{3}{2}a^{3}-\frac{13}{2}a^{2}-\frac{17}{2}a-3$ |
| 19.2-a6 |
19.2-a |
$6$ |
$8$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$6.09043$ |
$(1/2a^3-1/2a^2-1/2a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$54.35686508$ |
1.152363234 |
\( -\frac{735775933849957762097}{38} a^{3} - \frac{101952251559667760391}{38} a^{2} + \frac{3562800478876421131109}{38} a + \frac{1292462720633093698478}{19} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a + 1\) , \( a + 1\) , \( 5 a^{3} - 8 a^{2} - 16 a + 15\) , \( -9 a^{3} + 20 a^{2} + 29 a - 56\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a+1\right){x}^{2}+\left(5a^{3}-8a^{2}-16a+15\right){x}-9a^{3}+20a^{2}+29a-56$ |
| 29.1-a1 |
29.1-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( -29 \) |
$6.42101$ |
$(1/2a^3+1/2a^2-1/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$288.9003314$ |
1.531168694 |
\( -\frac{4012734681}{58} a^{3} + \frac{11061704843}{58} a^{2} + \frac{632240383}{58} a - \frac{4568350499}{29} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 2\) , \( a^{2} - 3\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - 1\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{1}{2}a-3\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-1$ |
| 29.1-a2 |
29.1-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$6.42101$ |
$(1/2a^3+1/2a^2-1/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$288.9003314$ |
1.531168694 |
\( \frac{99932939}{58} a^{3} - \frac{19709445}{58} a^{2} - \frac{250236317}{58} a + \frac{81455477}{29} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{17}{2} a - 4\) , \( 6 a^{3} - 29 a - 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-\frac{17}{2}a-4\right){x}+6a^{3}-29a-20$ |
| 29.1-a3 |
29.1-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( 29^{2} \) |
$6.42101$ |
$(1/2a^3+1/2a^2-1/2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$577.8006629$ |
1.531168694 |
\( -\frac{539857941}{1682} a^{3} - \frac{63606739}{1682} a^{2} + \frac{2596822069}{1682} a + \frac{940066182}{841} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 3 a^{3} - 6 a^{2} - 3 a - 1\) , \( \frac{19}{2} a^{3} - \frac{47}{2} a^{2} - \frac{15}{2} a + 20\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(3a^{3}-6a^{2}-3a-1\right){x}+\frac{19}{2}a^{3}-\frac{47}{2}a^{2}-\frac{15}{2}a+20$ |
| 29.1-a4 |
29.1-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.1 |
\( 29 \) |
\( - 29^{4} \) |
$6.42101$ |
$(1/2a^3+1/2a^2-1/2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$144.4501657$ |
1.531168694 |
\( -\frac{1061759562256497759}{1414562} a^{3} - \frac{147121931256461299}{1414562} a^{2} + \frac{5141290037660975785}{1414562} a + \frac{1865084993977686479}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{21}{2} a^{3} - \frac{47}{2} a^{2} - \frac{31}{2} a + 24\) , \( -8 a^{3} + 26 a^{2} - 9 a - 17\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(\frac{21}{2}a^{3}-\frac{47}{2}a^{2}-\frac{31}{2}a+24\right){x}-8a^{3}+26a^{2}-9a-17$ |
| 29.2-a1 |
29.2-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( - 29^{4} \) |
$6.42101$ |
$(a^2-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$144.4501657$ |
1.531168694 |
\( -\frac{344097316783618017}{707281} a^{3} + \frac{948538063540097546}{707281} a^{2} + \frac{54286274905112797}{707281} a - \frac{783553811115449441}{707281} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{25}{2} a^{3} + \frac{5}{2} a^{2} - \frac{115}{2} a - 42\) , \( -\frac{31}{2} a^{3} - \frac{3}{2} a^{2} + \frac{155}{2} a + 56\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}^{2}+\left(\frac{25}{2}a^{3}+\frac{5}{2}a^{2}-\frac{115}{2}a-42\right){x}-\frac{31}{2}a^{3}-\frac{3}{2}a^{2}+\frac{155}{2}a+56$ |
| 29.2-a2 |
29.2-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29^{2} \) |
$6.42101$ |
$(a^2-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$577.8006629$ |
1.531168694 |
\( -\frac{176483079}{841} a^{3} + \frac{478215419}{841} a^{2} + \frac{40825114}{841} a - \frac{381703735}{841} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 5 a^{3} - 25 a - 17\) , \( 13 a^{3} + 2 a^{2} - 62 a - 45\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a\right){x}^{2}+\left(5a^{3}-25a-17\right){x}+13a^{3}+2a^{2}-62a-45$ |
| 29.2-a3 |
29.2-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$6.42101$ |
$(a^2-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$288.9003314$ |
1.531168694 |
\( \frac{82412968}{29} a^{3} - \frac{122524715}{29} a^{2} - \frac{272020154}{29} a + \frac{346907209}{29} \) |
\( \bigl[a^{2} - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a + 1\) , \( a + 1\) , \( -3 a^{2} + 4 a + 5\) , \( \frac{7}{2} a^{3} - \frac{21}{2} a^{2} + \frac{1}{2} a + 8\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a+1\right){x}^{2}+\left(-3a^{2}+4a+5\right){x}+\frac{7}{2}a^{3}-\frac{21}{2}a^{2}+\frac{1}{2}a+8$ |
| 29.2-a4 |
29.2-a |
$4$ |
$4$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
29.2 |
\( 29 \) |
\( -29 \) |
$6.42101$ |
$(a^2-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$288.9003314$ |
1.531168694 |
\( -\frac{3095615715}{29} a^{3} - \frac{428869366}{29} a^{2} + \frac{14989828975}{29} a + \frac{10875578157}{29} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -a^{2} + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( 3 a^{3} - a^{2} - 13 a - 6\) , \( \frac{9}{2} a^{3} + \frac{1}{2} a^{2} - \frac{43}{2} a - 16\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(3a^{3}-a^{2}-13a-6\right){x}+\frac{9}{2}a^{3}+\frac{1}{2}a^{2}-\frac{43}{2}a-16$ |
| 59.1-a1 |
59.1-a |
$2$ |
$2$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( -59 \) |
$7.01714$ |
$(a^3-a^2-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$339.4348471$ |
1.799001091 |
\( -\frac{104018497}{118} a^{3} + \frac{287875093}{118} a^{2} + \frac{15899757}{118} a - \frac{118878462}{59} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( -a^{3} + 2 a^{2} - 1\) , \( a^{3} + 2 a^{2} - 8 a - 8\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-a^{3}+2a^{2}-1\right){x}+a^{3}+2a^{2}-8a-8$ |
| 59.1-a2 |
59.1-a |
$2$ |
$2$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{2} \) |
$7.01714$ |
$(a^3-a^2-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$169.7174235$ |
1.799001091 |
\( -\frac{30539913}{6962} a^{3} - \frac{11347457}{6962} a^{2} + \frac{156860547}{6962} a + \frac{63854737}{3481} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -a^{2} + 2\) , \( a^{2} - a - 3\) , \( a^{2} - a - 1\) , \( -\frac{7}{2} a^{3} - \frac{11}{2} a^{2} + \frac{9}{2} a + 5\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(a^{2}-a-1\right){x}-\frac{7}{2}a^{3}-\frac{11}{2}a^{2}+\frac{9}{2}a+5$ |
| 59.2-a1 |
59.2-a |
$2$ |
$2$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( -59 \) |
$7.01714$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$339.4348471$ |
1.799001091 |
\( -\frac{80084033}{59} a^{3} - \frac{11844265}{59} a^{2} + \frac{388329966}{59} a + \frac{284613459}{59} \) |
\( \bigl[a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 2\) , \( a + 1\) , \( -a^{3} + a^{2} + a + 1\) , \( \frac{3}{2} a^{3} - \frac{9}{2} a^{2} - \frac{1}{2} a + 3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+2\right){x}^{2}+\left(-a^{3}+a^{2}+a+1\right){x}+\frac{3}{2}a^{3}-\frac{9}{2}a^{2}-\frac{1}{2}a+3$ |
| 59.2-a2 |
59.2-a |
$2$ |
$2$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{2} \) |
$7.01714$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$169.7174235$ |
1.799001091 |
\( -\frac{9431597}{3481} a^{3} + \frac{30375282}{3481} a^{2} - \frac{4325613}{3481} a - \frac{29186969}{3481} \) |
\( \bigl[a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - 1\) , \( a^{2} - a - 2\) , \( -a^{2} + 4\) , \( -11 a^{3} + 20 a^{2} + 39 a - 55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a-1\right){x}^{2}+\left(-a^{2}+4\right){x}-11a^{3}+20a^{2}+39a-55$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
