| 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 |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -3 a - 1\) , \( -2 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-1\right){x}-2a-1$ |
| 1.1-a2 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}+a-1$ |
| 1.1-a3 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$5.639994193$ |
0.287814748 |
\( -77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 67 a - 161\) , \( 458 a - 1122\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(67a-161\right){x}+458a-1122$ |
| 1.1-a4 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( -77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -18 a - 41\) , \( 56 a + 138\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a-41\right){x}+56a+138$ |
| 1.1-a5 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$5.639994193$ |
0.287814748 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -68 a - 161\) , \( -459 a - 1122\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-68a-161\right){x}-459a-1122$ |
| 1.1-a6 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 17 a - 41\) , \( -57 a + 138\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-41\right){x}-57a+138$ |
| 10.1-a1 |
10.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$0.77847$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$35.64539671$ |
0.808454015 |
\( \frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -166 a - 413\) , \( 1827 a + 4480\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-166a-413\right){x}+1827a+4480$ |
| 10.1-a2 |
10.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$0.77847$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$35.64539671$ |
0.808454015 |
\( \frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a - 3\) , \( 5 a + 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-3\right){x}+5a+12$ |
| 10.1-a3 |
10.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{9} \) |
$0.77847$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$3.960599634$ |
0.808454015 |
\( -\frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a + 22\) , \( -133 a - 326\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(9a+22\right){x}-133a-326$ |
| 10.1-b1 |
10.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$0.77847$ |
$(-a+2), (-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.683258437$ |
1.255225901 |
\( \frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 117 a - 292\) , \( 1111 a - 2738\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(117a-292\right){x}+1111a-2738$ |
| 10.1-b2 |
10.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$0.77847$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$6.149325941$ |
1.255225901 |
\( \frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a - 2\) , \( 2 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a-2\right){x}+2a-4$ |
| 10.1-b3 |
10.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{9} \) |
$0.77847$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$6.149325941$ |
1.255225901 |
\( -\frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a + 23\) , \( -2 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a+23\right){x}-2a+7$ |
| 10.2-a1 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$35.64539671$ |
0.808454015 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 166 a - 413\) , \( -1827 a + 4480\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(166a-413\right){x}-1827a+4480$ |
| 10.2-a2 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$35.64539671$ |
0.808454015 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 3\) , \( -5 a + 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-3\right){x}-5a+12$ |
| 10.2-a3 |
10.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{9} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$3.960599634$ |
0.808454015 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a + 22\) , \( 133 a - 326\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a+22\right){x}+133a-326$ |
| 10.2-b1 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.683258437$ |
1.255225901 |
\( -\frac{2849985813237}{10} a - \frac{3491001283144}{5} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -117 a - 292\) , \( -1111 a - 2738\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-117a-292\right){x}-1111a-2738$ |
| 10.2-b2 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$6.149325941$ |
1.255225901 |
\( -\frac{1061271}{500} a - \frac{656416}{125} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( -2 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}-2a-4$ |
| 10.2-b3 |
10.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{9} \) |
$0.77847$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{4} \) |
$1$ |
$6.149325941$ |
1.255225901 |
\( \frac{21355471243}{62500000} a + \frac{1734442691}{1953125} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 23\) , \( 2 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(8a+23\right){x}+2a+7$ |
| 16.1-a1 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 6\) , \( 6 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-6\right){x}+6a-16$ |
| 16.1-a2 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 6\) , \( -6 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-6\right){x}-6a-16$ |
| 16.1-a3 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$2.819997096$ |
1.295166367 |
\( -77092288000 a + 188837384000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 264 a - 646\) , \( 3782 a - 9264\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(264a-646\right){x}+3782a-9264$ |
| 16.1-a4 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( -77092288000 a + 188837384000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -64 a - 166\) , \( 418 a + 1056\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-64a-166\right){x}+418a+1056$ |
| 16.1-a5 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 64 a - 166\) , \( -418 a + 1056\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(64a-166\right){x}-418a+1056$ |
| 16.1-a6 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$2.819997096$ |
1.295166367 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -264 a - 646\) , \( -3782 a - 9264\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-264a-646\right){x}-3782a-9264$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$0.95869$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$10.38577982$ |
2.119988428 |
\( -\frac{66417408}{23} a + \frac{162689472}{23} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( a - 1\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}-1$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$0.95869$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$20.77155964$ |
2.119988428 |
\( \frac{1596672}{529} a + \frac{6322752}{529} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 11 a - 23\) , \( 20 a - 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(11a-23\right){x}+20a-47$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$0.95869$ |
$(-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.156973252$ |
$42.58064027$ |
0.682185096 |
\( -\frac{66417408}{23} a + \frac{162689472}{23} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 10 a + 23\) , \( 197 a + 482\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(10a+23\right){x}+197a+482$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$0.95869$ |
$(-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.078486626$ |
$42.58064027$ |
0.682185096 |
\( \frac{1596672}{529} a + \frac{6322752}{529} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+{x}$ |
| 23.2-a1 |
23.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$0.95869$ |
$(2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$20.77155964$ |
2.119988428 |
\( -\frac{1596672}{529} a + \frac{6322752}{529} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -12 a - 23\) , \( -20 a - 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-12a-23\right){x}-20a-47$ |
| 23.2-a2 |
23.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$0.95869$ |
$(2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$10.38577982$ |
2.119988428 |
\( \frac{66417408}{23} a + \frac{162689472}{23} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -2 a - 1\) , \( -a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a-1\right){x}-a-1$ |
| 23.2-b1 |
23.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$0.95869$ |
$(2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.078486626$ |
$42.58064027$ |
0.682185096 |
\( -\frac{1596672}{529} a + \frac{6322752}{529} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$ |
| 23.2-b2 |
23.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$0.95869$ |
$(2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.156973252$ |
$42.58064027$ |
0.682185096 |
\( \frac{66417408}{23} a + \frac{162689472}{23} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -11 a + 23\) , \( -198 a + 482\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11a+23\right){x}-198a+482$ |
| 24.1-a1 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.683508517$ |
1.160141318 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 1\) , \( 21\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+{x}+21$ |
| 24.1-a2 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.36701703$ |
1.160141318 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a + 35\) , \( 67 a - 164\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a+35\right){x}+67a-164$ |
| 24.1-a3 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$22.73403407$ |
1.160141318 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -4\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-4{x}-2$ |
| 24.1-a4 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$22.73403407$ |
1.160141318 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-9{x}+3$ |
| 24.1-a5 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.683508517$ |
1.160141318 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -19\) , \( -29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-19{x}-29$ |
| 24.1-a6 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.73403407$ |
1.160141318 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -99\) , \( 345\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-99{x}+345$ |
| 24.1-b1 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.079273864$ |
$2.325279868$ |
1.024545539 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -78 a + 194\) , \( 4376 a - 10718\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-78a+194\right){x}+4376a-10718$ |
| 24.1-b2 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539636932$ |
$18.60223895$ |
1.024545539 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.079273864$ |
$37.20447790$ |
1.024545539 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 22 a - 51\) , \( -78 a + 192\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22a-51\right){x}-78a+192$ |
| 24.1-b4 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$9.301119475$ |
1.024545539 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 122 a - 296\) , \( 1012 a - 2478\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(122a-296\right){x}+1012a-2478$ |
| 24.1-b5 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$37.20447790$ |
1.024545539 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -322 a - 786\) , \( 5124 a + 12552\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-322a-786\right){x}+5124a+12552$ |
| 24.1-b6 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0.96894$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.079273864$ |
$2.325279868$ |
1.024545539 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1922 a - 4706\) , \( -70528 a - 172758\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1922a-4706\right){x}-70528a-172758$ |
| 25.2-a1 |
25.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$10.14732862$ |
2.071314782 |
\( -118784 a - 290816 \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -a - 2\) , \( -a - 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-2\right){x}-a-3$ |
| 25.2-a2 |
25.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$10.14732862$ |
2.071314782 |
\( 1835626496 a - 4496347136 \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 19 a - 12\) , \( -31 a + 117\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(19a-12\right){x}-31a+117$ |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.99242927$ |
2.447944375 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -2 a + 2\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+2\right){x}+5$ |
| 25.2-b2 |
25.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.98485855$ |
2.447944375 |
\( \frac{8704256}{25} a + \frac{21394496}{25} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 75 a - 188\) , \( -347 a + 847\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(75a-188\right){x}-347a+847$ |
| 25.2-c1 |
25.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$29.38675386$ |
0.239941840 |
\( -118784 a - 290816 \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -3 a + 8\) , \( 13 a - 32\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+8\right){x}+13a-32$ |
| 25.2-c2 |
25.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.175470154$ |
0.239941840 |
\( 1835626496 a - 4496347136 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 685 a + 1678\) , \( -11772 a - 28836\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(685a+1678\right){x}-11772a-28836$ |
*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.
