| 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 |
| 4.1-a1 |
4.1-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{17} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( \frac{1490538551}{131072} a^{2} - \frac{6302729347}{131072} a + \frac{2281468939}{65536} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a + 1\) , \( -\frac{5428030616875785839596918747}{2} a^{2} - \frac{12468569243927383201124102147}{2} a + 6585276892125508253156416809\) , \( \frac{1778982535081918822466482707329914974773289}{2} a^{2} + \frac{4086448380273381716620242365952758476908693}{2} a - 2158258382579403676916897791908160856855144\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}^{2}+\left(-\frac{5428030616875785839596918747}{2}a^{2}-\frac{12468569243927383201124102147}{2}a+6585276892125508253156416809\right){x}+\frac{1778982535081918822466482707329914974773289}{2}a^{2}+\frac{4086448380273381716620242365952758476908693}{2}a-2158258382579403676916897791908160856855144$ |
| 4.1-a2 |
4.1-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$50.99304271$ |
1.644936861 |
\( \frac{1660785660611}{512} a^{2} - \frac{6782432850673}{512} a + \frac{1077075166079}{128} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( 1\) , \( 1260592332 a^{2} + 2895669924 a - 3058696978\) , \( \frac{5289755763677}{2} a^{2} + \frac{12150942138947}{2} a - 6417522086220\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}^{2}+\left(1260592332a^{2}+2895669924a-3058696978\right){x}+\frac{5289755763677}{2}a^{2}+\frac{12150942138947}{2}a-6417522086220$ |
| 4.1-a3 |
4.1-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{5} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( \frac{212068284953}{32} a^{2} + \frac{487135796771}{32} a - \frac{257280852307}{16} \) |
\( \bigl[1\) , \( a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{6151408334958753821769050847112196849}{2} a^{2} - \frac{14130218892584489931013217519954906083}{2} a + 7462877426720882640138607519245152578\) , \( \frac{16618716709396809372366318063381491518225891025259152029}{2} a^{2} + \frac{38174364638273178291400194444212921470457543144134251711}{2} a - 20161796947667300676602389656879723718330935346799904418\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{6151408334958753821769050847112196849}{2}a^{2}-\frac{14130218892584489931013217519954906083}{2}a+7462877426720882640138607519245152578\right){x}+\frac{16618716709396809372366318063381491518225891025259152029}{2}a^{2}+\frac{38174364638273178291400194444212921470457543144134251711}{2}a-20161796947667300676602389656879723718330935346799904418$ |
| 4.1-a4 |
4.1-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$12.74826067$ |
1.644936861 |
\( -10001930873667606 a^{2} + \frac{8529574032310645}{4} a + \frac{406788319277484817}{4} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -10 a^{2} + 29 a - 16\) , \( 197 a^{2} - 828 a + 528\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-10a^{2}+29a-16\right){x}+197a^{2}-828a+528$ |
| 4.1-a5 |
4.1-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{10} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$203.9721708$ |
1.644936861 |
\( \frac{9503751}{512} a^{2} + \frac{24037613}{512} a - \frac{7684773}{256} \) |
\( \bigl[1\) , \( -a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{19147065154823509537296697}{2} a^{2} - \frac{43982159378149527796839635}{2} a + 23229184692523661951257835\) , \( 45510003933407442394057701639672773911 a^{2} + 104539689509287006903773126858614659987 a - 110425308336121793763398860920944935407\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-\frac{19147065154823509537296697}{2}a^{2}-\frac{43982159378149527796839635}{2}a+23229184692523661951257835\right){x}+45510003933407442394057701639672773911a^{2}+104539689509287006903773126858614659987a-110425308336121793763398860920944935407$ |
| 4.1-a6 |
4.1-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( -\frac{513159655}{16} a^{2} + \frac{54348725}{8} a + \frac{5220035937}{16} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( a\) , \( -87731935950 a^{2} - 201526445871 a + 212872450913\) , \( 1533516070186697 a^{2} + 3522594594133587 a - 3720917825815819\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-87731935950a^{2}-201526445871a+212872450913\right){x}+1533516070186697a^{2}+3522594594133587a-3720917825815819$ |
| 4.2-a1 |
4.2-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.49015$ |
$(-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$12.74826067$ |
1.644936861 |
\( \frac{31478149462359779}{8} a^{2} - \frac{128552744516321917}{8} a + \frac{40829380460023157}{4} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -10 a^{2} - 29 a + 3\) , \( 315 a^{2} + 710 a - 811\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-10a^{2}-29a+3\right){x}+315a^{2}+710a-811$ |
| 4.2-a2 |
4.2-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{10} \) |
$3.49015$ |
$(-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$203.9721708$ |
1.644936861 |
\( -\frac{8385341}{256} a^{2} + \frac{559205}{128} a + \frac{10988651}{32} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 2\) , \( a\) , \( -\frac{2651715352000568223681}{2} a^{2} - \frac{6091177227116397860417}{2} a + 3217056251991919078985\) , \( -291886460524015678667569665688 a^{2} - 670483790768170189034127062001 a + 708232248225393919732739215117\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+2\right){x}^{2}+\left(-\frac{2651715352000568223681}{2}a^{2}-\frac{6091177227116397860417}{2}a+3217056251991919078985\right){x}-291886460524015678667569665688a^{2}-670483790768170189034127062001a+708232248225393919732739215117$ |
| 4.2-a3 |
4.2-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.49015$ |
$(-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( \frac{404462205}{32} a^{2} - \frac{1648176415}{32} a + \frac{523229187}{16} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( 1\) , \( -\frac{25183717652763}{2} a^{2} - \frac{57848776017723}{2} a + 30552840546066\) , \( 68621338518021789940 a^{2} + 157628055424528863595 a - 166502566674742082219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{25183717652763}{2}a^{2}-\frac{57848776017723}{2}a+30552840546066\right){x}+68621338518021789940a^{2}+157628055424528863595a-166502566674742082219$ |
| 4.2-a4 |
4.2-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{5} \) |
$3.49015$ |
$(-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( -\frac{174801020431}{16} a^{2} + \frac{18633632261}{8} a + 111083260375 \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( a + 1\) , \( \frac{38132434966148964565}{2} a^{2} + \frac{87592893145588972825}{2} a - 46262200887804228516\) , \( -503349020026853863923534404 a^{2} - 1156228207437806068526293031 a + 1221324234963398073257804273\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(\frac{38132434966148964565}{2}a^{2}+\frac{87592893145588972825}{2}a-46262200887804228516\right){x}-503349020026853863923534404a^{2}-1156228207437806068526293031a+1221324234963398073257804273$ |
| 4.2-a5 |
4.2-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{10} \) |
$3.49015$ |
$(-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$50.99304271$ |
1.644936861 |
\( \frac{2560823595031}{512} a^{2} + \frac{5882394916253}{512} a - \frac{3106787066133}{256} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( a + 1\) , \( -\frac{194866736477981787}{2} a^{2} - \frac{447622640439772429}{2} a + 236411970997865516\) , \( 46850283123534020826438292 a^{2} + 107618405358149835384910554 a - 113677356897637570801804441\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{194866736477981787}{2}a^{2}-\frac{447622640439772429}{2}a+236411970997865516\right){x}+46850283123534020826438292a^{2}+107618405358149835384910554a-113677356897637570801804441$ |
| 4.2-a6 |
4.2-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{17} \) |
$3.49015$ |
$(-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( \frac{1203047699}{65536} a^{2} + \frac{1346793125}{32768} a - \frac{358912125}{8192} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( a + 1\) , \( -293666766415188423468504311958865 a^{2} - 674573278990739510836315139647475 a + 712551975976967533186515000387691\) , \( -7729309292636733869398991628386252903011108951282 a^{2} - 17754768704389180046884576095022332783828877605582 a + 18754368009142871216787193633464282747126603172865\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-293666766415188423468504311958865a^{2}-674573278990739510836315139647475a+712551975976967533186515000387691\right){x}-7729309292636733869398991628386252903011108951282a^{2}-17754768704389180046884576095022332783828877605582a+18754368009142871216787193633464282747126603172865$ |
| 4.3-a1 |
4.3-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{5} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( \frac{137533755909}{32} a^{2} - \frac{561670325815}{32} a + \frac{89195509889}{8} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1370274757167}{2} a^{2} + \frac{3147617782375}{2} a - 1662414848242\) , \( -5990529133777695795 a^{2} - 13760668018350788183 a + 14535398143710820105\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}^{2}+\left(\frac{1370274757167}{2}a^{2}+\frac{3147617782375}{2}a-1662414848242\right){x}-5990529133777695795a^{2}-13760668018350788183a+14535398143710820105$ |
| 4.3-a2 |
4.3-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{10} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (a^2-11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$50.99304271$ |
1.644936861 |
\( -\frac{2110804627821}{256} a^{2} + \frac{225009483605}{128} a + \frac{2682765092691}{32} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{46962928797615074395}{2} a^{2} - \frac{107877160418031369127}{2} a + 56975339976153873142\) , \( -184013821751192998303469378092 a^{2} - 422692729700379500788381417697 a + 446490469100301207036576481755\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}^{2}+\left(-\frac{46962928797615074395}{2}a^{2}-\frac{107877160418031369127}{2}a+56975339976153873142\right){x}-184013821751192998303469378092a^{2}-422692729700379500788381417697a+446490469100301207036576481755$ |
| 4.3-a3 |
4.3-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{17} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( -\frac{3896633949}{131072} a^{2} + \frac{915556847}{131072} a + \frac{9966762495}{32768} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -\frac{43450431}{2} a^{2} - \frac{99808667}{2} a + 52713969\) , \( 117746423354 a^{2} + 270471840481 a - 285699493946\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{43450431}{2}a^{2}-\frac{99808667}{2}a+52713969\right){x}+117746423354a^{2}+270471840481a-285699493946$ |
| 4.3-a4 |
4.3-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( - 2^{4} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$12.74826067$ |
1.644936861 |
\( \frac{48537297526981069}{8} a^{2} + \frac{111493596451700627}{8} a - \frac{29442680630410891}{2} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( \frac{39}{2} a^{2} - \frac{1}{2} a - 213\) , \( -\frac{1025}{2} a^{2} + \frac{235}{2} a + 5179\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{39}{2}a^{2}-\frac{1}{2}a-213\right){x}-\frac{1025}{2}a^{2}+\frac{235}{2}a+5179$ |
| 4.3-a5 |
4.3-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{10} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$203.9721708$ |
1.644936861 |
\( \frac{7266931}{512} a^{2} - \frac{26274433}{512} a + \frac{4264719}{128} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -\frac{4178954957}{2} a^{2} - \frac{9599354341}{2} a + 5069900570\) , \( -140055991389626 a^{2} - 321718492382707 a + 339831349084279\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-\frac{4178954957}{2}a^{2}-\frac{9599354341}{2}a+5069900570\right){x}-140055991389626a^{2}-321718492382707a+339831349084279$ |
| 4.3-a6 |
4.3-a |
$6$ |
$8$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
4.3 |
\( 2^{2} \) |
\( 2^{8} \) |
$3.49015$ |
$(-1/2a^2-1/2a+3), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$101.9860854$ |
1.644936861 |
\( \frac{621857105}{32} a^{2} + \frac{1430781515}{32} a - \frac{375406309}{8} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{2369322221}{2} a^{2} - \frac{5442500283}{2} a + 2874457422\) , \( -\frac{125623004119037}{2} a^{2} - \frac{288564902456265}{2} a + 152405600582377\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{2369322221}{2}a^{2}-\frac{5442500283}{2}a+2874457422\right){x}-\frac{125623004119037}{2}a^{2}-\frac{288564902456265}{2}a+152405600582377$ |
| 8.1-a1 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$106.3151676$ |
1.143173845 |
\( \frac{15435701143}{8192} a^{2} + \frac{35497853597}{8192} a - \frac{18652209429}{4096} \) |
\( \bigl[1\) , \( -a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -48431 a^{2} - 111250 a + 117514\) , \( 16467349 a^{2} + 37826662 a - 39956316\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}-a{x}^{2}+\left(-48431a^{2}-111250a+117514\right){x}+16467349a^{2}+37826662a-39956316$ |
| 8.1-a2 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{22} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$3.937598801$ |
1.143173845 |
\( -\frac{8184071106463885}{8192} a^{2} + \frac{1736311114468991}{8192} a + \frac{20810407550974991}{2048} \) |
\( \bigl[1\) , \( -a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{173677}{2} a^{2} - \frac{398945}{2} a + 210704\) , \( -12943605 a^{2} - 29732369 a + 31406312\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}-a{x}^{2}+\left(-\frac{173677}{2}a^{2}-\frac{398945}{2}a+210704\right){x}-12943605a^{2}-29732369a+31406312$ |
| 8.1-a3 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$26.57879191$ |
1.143173845 |
\( \frac{7295623413890681}{128} a^{2} + \frac{16758576697574963}{128} a - \frac{8851013876269547}{64} \) |
\( \bigl[1\) , \( -a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -774891 a^{2} - 1779980 a + 1880194\) , \( 1051566715 a^{2} + 2415522926 a - 2551517660\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}-a{x}^{2}+\left(-774891a^{2}-1779980a+1880194\right){x}+1051566715a^{2}+2415522926a-2551517660$ |
| 8.1-a4 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$0.984399700$ |
1.143173845 |
\( -\frac{1241964632137526614402953477}{128} a^{2} + \frac{264784605316078371925020983}{128} a + \frac{3156994832360291977213522431}{32} \) |
\( \bigl[1\) , \( -a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1553617}{2} a^{2} - \frac{3568765}{2} a + 1884844\) , \( 1046107681 a^{2} + 2402983145 a - 2538271884\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}-a{x}^{2}+\left(-\frac{1553617}{2}a^{2}-\frac{3568765}{2}a+1884844\right){x}+1046107681a^{2}+2402983145a-2538271884$ |
| 8.1-a5 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{17} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$0.984399700$ |
1.143173845 |
\( \frac{912562886213935378219}{512} a^{2} - \frac{3726790347255236525503}{512} a + \frac{1183658439586182674803}{256} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( 6601 a^{2} - 4 a - 71745\) , \( \frac{1369511}{2} a^{2} - \frac{189539}{2} a - 7131293\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(6601a^{2}-4a-71745\right){x}+\frac{1369511}{2}a^{2}-\frac{189539}{2}a-7131293$ |
| 8.1-a6 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$26.57879191$ |
1.143173845 |
\( \frac{4787876636631}{33554432} a^{2} - \frac{19617344369827}{33554432} a + \frac{6235831901995}{16777216} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{103}{2} a^{2} + \frac{57}{2} a + 465\) , \( \frac{7051}{2} a^{2} - \frac{1359}{2} a - 36085\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{103}{2}a^{2}+\frac{57}{2}a+465\right){x}+\frac{7051}{2}a^{2}-\frac{1359}{2}a-36085$ |
| 8.1-a7 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$212.6303352$ |
1.143173845 |
\( \frac{761247}{512} a^{2} - \frac{2557213}{512} a + \frac{842517}{128} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( a + 1\) , \( -\frac{7303374230203}{2} a^{2} - \frac{16776365818661}{2} a + 8860440359931\) , \( \frac{18302408952526744619}{2} a^{2} + \frac{42041924495739881721}{2} a - 22204449321009330401\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{7303374230203}{2}a^{2}-\frac{16776365818661}{2}a+8860440359931\right){x}+\frac{18302408952526744619}{2}a^{2}+\frac{42041924495739881721}{2}a-22204449321009330401$ |
| 8.1-a8 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{38} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$7.875197603$ |
1.143173845 |
\( -\frac{8683325419613}{33554432} a^{2} + \frac{6360148347887}{33554432} a + \frac{26238213839871}{8388608} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 3\) , \( a + 1\) , \( -80318829963119 a^{2} - 184498018466003 a + 194885317453541\) , \( -\frac{2215679628642342460229}{2} a^{2} - \frac{5089572410700083948617}{2} a + 2688058503850097230579\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+3\right){x}^{2}+\left(-80318829963119a^{2}-184498018466003a+194885317453541\right){x}-\frac{2215679628642342460229}{2}a^{2}-\frac{5089572410700083948617}{2}a+2688058503850097230579$ |
| 8.1-a9 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{21} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$106.3151676$ |
1.143173845 |
\( -\frac{102357882493}{131072} a^{2} + \frac{21829616975}{131072} a + \frac{260192735071}{32768} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( 1\) , \( 23395985239 a^{2} + 53742228549 a - 56767933650\) , \( \frac{21978208854617395}{2} a^{2} + \frac{50485496177805725}{2} a - 26663923090383003\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(23395985239a^{2}+53742228549a-56767933650\right){x}+\frac{21978208854617395}{2}a^{2}+\frac{50485496177805725}{2}a-26663923090383003$ |
| 8.1-a10 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{55} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.937598801$ |
1.143173845 |
\( -\frac{166564119831074301}{562949953421312} a^{2} - \frac{177118555281457}{562949953421312} a + \frac{395645725632682463}{140737488355328} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( 1\) , \( -\frac{435680755967}{2} a^{2} - \frac{1000789431277}{2} a + 528567102350\) , \( -\frac{718024986615993689}{2} a^{2} - \frac{1649354046872433655}{2} a + 871106610495235965\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{435680755967}{2}a^{2}-\frac{1000789431277}{2}a+528567102350\right){x}-\frac{718024986615993689}{2}a^{2}-\frac{1649354046872433655}{2}a+871106610495235965$ |
| 8.1-a11 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$106.3151676$ |
1.143173845 |
\( \frac{12970883659}{256} a^{2} - \frac{26485227727}{128} a + \frac{4205966099}{32} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( 1\) , \( -\frac{653416585817190364335837}{2} a^{2} - \frac{1500943992479085874746153}{2} a + 792723815915048538887161\) , \( -\frac{525131349070704485554320356626542077}{2} a^{2} - \frac{1206263753872063985052579579870102855}{2} a + 637088399541195815961754869125588709\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{653416585817190364335837}{2}a^{2}-\frac{1500943992479085874746153}{2}a+792723815915048538887161\right){x}-\frac{525131349070704485554320356626542077}{2}a^{2}-\frac{1206263753872063985052579579870102855}{2}a+637088399541195815961754869125588709$ |
| 8.1-a12 |
8.1-a |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{37} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.937598801$ |
1.143173845 |
\( \frac{923315876475536883}{16777216} a^{2} + \frac{1060460844671671493}{8388608} a - \frac{280041287382554013}{2097152} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( 1\) , \( -25816568498103096891250431 a^{2} - 59302479053529450149481354 a + 62641228085918928774138701\) , \( -\frac{404136820231561935056744756588322747281}{2} a^{2} - \frac{928330785646556865847533354427581874087}{2} a + 490298056767369808630550554198180375977\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-25816568498103096891250431a^{2}-59302479053529450149481354a+62641228085918928774138701\right){x}-\frac{404136820231561935056744756588322747281}{2}a^{2}-\frac{928330785646556865847533354427581874087}{2}a+490298056767369808630550554198180375977$ |
| 8.1-b1 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{21} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$106.3151676$ |
1.143173845 |
\( \frac{31046874867}{65536} a^{2} + \frac{35655503813}{32768} a - \frac{9415913629}{8192} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( 1\) , \( -1135109791368193534983394005464443834733 a^{2} - 2607427266370219506706960083397912465123 a + 2754226277163030434341509109058261333234\) , \( \frac{117811584109046276883299513841731085218549732515082878509077}{2} a^{2} + \frac{270621519641666655481323447437691739592121577435103658894241}{2} a - 142928800004548125107107810894785053131335568678444287097840\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}^{2}+\left(-1135109791368193534983394005464443834733a^{2}-2607427266370219506706960083397912465123a+2754226277163030434341509109058261333234\right){x}+\frac{117811584109046276883299513841731085218549732515082878509077}{2}a^{2}+\frac{270621519641666655481323447437691739592121577435103658894241}{2}a-142928800004548125107107810894785053131335568678444287097840$ |
| 8.1-b2 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{55} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.937598801$ |
1.143173845 |
\( \frac{41596750318948211}{281474976710656} a^{2} + \frac{62483684756063045}{140737488355328} a - \frac{15568191246577693}{35184372088832} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( 1\) , \( -\frac{5171878668446132260474771433238959743711}{2} a^{2} - \frac{11880170148308365383903785310394241017191}{2} a + 6274513813224967158312755214749080503789\) , \( -\frac{237076263554909853535311735052515444474061429406286932174419}{2} a^{2} - \frac{544580901779687961756431103089298691196301520328621842187519}{2} a + 287620492634249855289661836746352099769467748294166719671064\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}^{2}+\left(-\frac{5171878668446132260474771433238959743711}{2}a^{2}-\frac{11880170148308365383903785310394241017191}{2}a+6274513813224967158312755214749080503789\right){x}-\frac{237076263554909853535311735052515444474061429406286932174419}{2}a^{2}-\frac{544580901779687961756431103089298691196301520328621842187519}{2}a+287620492634249855289661836746352099769467748294166719671064$ |
| 8.1-b3 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$106.3151676$ |
1.143173845 |
\( \frac{10031076227}{8192} a^{2} - \frac{40902478513}{8192} a + \frac{6498683231}{2048} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 0\) , \( -\frac{290659894099451}{2} a^{2} - \frac{667666281163597}{2} a + 352628055952723\) , \( -\frac{5182308369239675957581}{2} a^{2} - \frac{11904127906787736882423}{2} a + 6287167107297033020275\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{290659894099451}{2}a^{2}-\frac{667666281163597}{2}a+352628055952723\right){x}-\frac{5182308369239675957581}{2}a^{2}-\frac{11904127906787736882423}{2}a+6287167107297033020275$ |
| 8.1-b4 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{9} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$26.57879191$ |
1.143173845 |
\( \frac{4731476641842141}{128} a^{2} - \frac{19322723469623503}{128} a + \frac{3068524926883377}{32} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 0\) , \( -\frac{4598803458049401}{2} a^{2} - \frac{10563775962801247}{2} a + 5579260008144613\) , \( -\frac{339705134435254243903407}{2} a^{2} - \frac{780326658080188882638293}{2} a + 412129652507459572293105\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(-\frac{4598803458049401}{2}a^{2}-\frac{10563775962801247}{2}a+5579260008144613\right){x}-\frac{339705134435254243903407}{2}a^{2}-\frac{780326658080188882638293}{2}a+412129652507459572293105$ |
| 8.1-b5 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{22} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$3.937598801$ |
1.143173845 |
\( \frac{2480095555233219}{4096} a^{2} + \frac{2851987775615333}{2048} a - \frac{749505331913109}{512} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 0\) , \( -11640715115070153 a^{2} - 26739543806151996 a + 28244988897726338\) , \( -1934729019815212481233845 a^{2} - 4444209042742355035177206 a + 4694419470333400298464428\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(-11640715115070153a^{2}-26739543806151996a+28244988897726338\right){x}-1934729019815212481233845a^{2}-4444209042742355035177206a+4694419470333400298464428$ |
| 8.1-b6 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{11} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$0.984399700$ |
1.143173845 |
\( \frac{376687309363401246581993615}{64} a^{2} + \frac{432638661387062683910479931}{32} a - \frac{57124545000620623917295671}{4} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( 0\) , \( -186251441836518743 a^{2} - 427832700887856906 a + 451919822352450978\) , \( -123822656467410908828823299 a^{2} - 284429376896102334095825124 a + 300442844158369935042576620\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}^{2}+\left(-186251441836518743a^{2}-427832700887856906a+451919822352450978\right){x}-123822656467410908828823299a^{2}-284429376896102334095825124a+300442844158369935042576620$ |
| 8.1-b7 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$26.57879191$ |
1.143173845 |
\( -\frac{12202610503229}{33554432} a^{2} + \frac{2626857229967}{33554432} a + \frac{30997584979103}{8388608} \) |
\( \bigl[1\) , \( a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{291}{2} a^{2} + \frac{1195}{2} a - 379\) , \( 4122 a^{2} - 16863 a + 10715\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{291}{2}a^{2}+\frac{1195}{2}a-379\right){x}+4122a^{2}-16863a+10715$ |
| 8.1-b8 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{17} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{4} \) |
$1$ |
$0.984399700$ |
1.143173845 |
\( -\frac{2319676616734585951861}{512} a^{2} + \frac{494550844306715195423}{512} a + \frac{5896469917322841021631}{128} \) |
\( \bigl[1\) , \( a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( 952 a^{2} - 4365 a + 2846\) , \( -\frac{49237}{2} a^{2} + \frac{187547}{2} a - 58542\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(952a^{2}-4365a+2846\right){x}-\frac{49237}{2}a^{2}+\frac{187547}{2}a-58542$ |
| 8.1-b9 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$212.6303352$ |
1.143173845 |
\( -\frac{829615}{256} a^{2} + \frac{4273}{16} a + \frac{151683}{4} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( a\) , \( -\frac{7678162178811026347458451685}{2} a^{2} - \frac{17637280175790951695390675557}{2} a + 9315132418913798458350597914\) , \( \frac{526617387685626106626406919508732879254725}{2} a^{2} + \frac{1209677289402186839931218437956311134469673}{2} a - 638891258891551150998436909827864158844910\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-\frac{7678162178811026347458451685}{2}a^{2}-\frac{17637280175790951695390675557}{2}a+9315132418913798458350597914\right){x}+\frac{526617387685626106626406919508732879254725}{2}a^{2}+\frac{1209677289402186839931218437956311134469673}{2}a-638891258891551150998436909827864158844910$ |
| 8.1-b10 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{38} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$7.875197603$ |
1.143173845 |
\( \frac{3760868441875}{16777216} a^{2} + \frac{2461228488869}{8388608} a - \frac{602760581245}{2097152} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( a\) , \( -113227327885953618199340699570 a^{2} - 260091159703786472290883548176 a + 274734377350897498613978932469\) , \( -58675542582380663838808188825611335618273306 a^{2} - 134781860540519656949244079109777685492283075 a + 142370123521180517857670856726860117014532717\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+3\right){x}^{2}+\left(-113227327885953618199340699570a^{2}-260091159703786472290883548176a+274734377350897498613978932469\right){x}-58675542582380663838808188825611335618273306a^{2}-134781860540519656949244079109777685492283075a+142370123521180517857670856726860117014532717$ |
| 8.1-b11 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$106.3151676$ |
1.143173845 |
\( -\frac{65941339113}{512} a^{2} + \frac{14057804477}{512} a + \frac{335238815403}{256} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( 4841025955948432551612875082052 a^{2} + 11120178127907208292105204635706 a - 11746247805888725218854205228202\) , \( 18406962047941626729657033747703716410221802672 a^{2} + 42282090331539410371457331633715753296566106596 a - 44662585893190469129710211765563810396450395964\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(4841025955948432551612875082052a^{2}+11120178127907208292105204635706a-11746247805888725218854205228202\right){x}+18406962047941626729657033747703716410221802672a^{2}+42282090331539410371457331633715753296566106596a-44662585893190469129710211765563810396450395964$ |
| 8.1-b12 |
8.1-b |
$12$ |
$24$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{37} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.937598801$ |
1.143173845 |
\( \frac{1197605812867806103}{33554432} a^{2} - \frac{4890869318769953635}{33554432} a + \frac{1553379274140444651}{16777216} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( -\frac{94775353971045403527636848619821}{2} a^{2} - \frac{217705673938491314452696490730293}{2} a + 114981287413549444636577410102373\) , \( -\frac{1600052624330384921429740342395508378240880850165}{2} a^{2} - \frac{3675433752780483578493260129267123193602855046217}{2} a + 1941180939626373291512461272087926557125182622323\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(-\frac{94775353971045403527636848619821}{2}a^{2}-\frac{217705673938491314452696490730293}{2}a+114981287413549444636577410102373\right){x}-\frac{1600052624330384921429740342395508378240880850165}{2}a^{2}-\frac{3675433752780483578493260129267123193602855046217}{2}a+1941180939626373291512461272087926557125182622323$ |
| 8.1-c1 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2^{2} \) |
$1$ |
$0.065966108$ |
5.109181533 |
\( \frac{212123289329879682518657639836587}{32} a^{2} - \frac{866284438086857798891460365175369}{32} a + \frac{137569435181617730718433084631595}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -\frac{430193}{2} a^{2} + \frac{1574293}{2} a - 486172\) , \( -174690080 a^{2} + 696616698 a - 439956149\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-\frac{430193}{2}a^{2}+\frac{1574293}{2}a-486172\right){x}-174690080a^{2}+696616698a-439956149$ |
| 8.1-c2 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 7$ |
2Cs, 7B.1.1 |
$1$ |
\( 2^{3} \cdot 7^{3} \) |
$1$ |
$45.25275072$ |
5.109181533 |
\( \frac{42396561}{16384} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( \frac{12321}{2} a^{2} - \frac{2627}{2} a - 62639\) , \( -335922 a^{2} + 71618 a + 3415569\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(\frac{12321}{2}a^{2}-\frac{2627}{2}a-62639\right){x}-335922a^{2}+71618a+3415569$ |
| 8.1-c3 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$22.62637536$ |
5.109181533 |
\( -\frac{162946107833949}{536870912} a^{2} + \frac{31406299407855}{536870912} a + \frac{417097255163391}{134217728} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3104 a^{2} - 656 a - 31580\) , \( -208352 a^{2} + 44432 a + 2118431\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3104a^{2}-656a-31580\right){x}-208352a^{2}+44432a+2118431$ |
| 8.1-c4 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$22.62637536$ |
5.109181533 |
\( \frac{65769904213047}{536870912} a^{2} - \frac{260122311454851}{536870912} a + \frac{82276569972747}{268435456} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -200 a^{2} - 283 a + 1029\) , \( -2695 a^{2} - 4935 a + 10411\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-200a^{2}-283a+1029\right){x}-2695a^{2}-4935a+10411$ |
| 8.1-c5 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 7$ |
2Cs, 7B.1.3 |
$2401$ |
\( 2^{3} \) |
$1$ |
$0.131932217$ |
5.109181533 |
\( \frac{51181724570498001}{4} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3979097 a^{2} - 9140104 a + 9654727\) , \( -12226103294 a^{2} - 28084220182 a + 29665371405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3979097a^{2}-9140104a+9654727\right){x}-12226103294a^{2}-28084220182a+29665371405$ |
| 8.1-c6 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{42} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7^{3} \) |
$1$ |
$22.62637536$ |
5.109181533 |
\( \frac{48588101810451}{268435456} a^{2} + \frac{57179003011749}{134217728} a - \frac{13639816483965}{33554432} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -\frac{21177514163}{2} a^{2} - \frac{48646243987}{2} a + 25692521743\) , \( 1678001156646822 a^{2} + 3854487030340920 a - 4071495915100901\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-\frac{21177514163}{2}a^{2}-\frac{48646243987}{2}a+25692521743\right){x}+1678001156646822a^{2}+3854487030340920a-4071495915100901$ |
| 8.1-c7 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2^{2} \) |
$1$ |
$0.065966108$ |
5.109181533 |
\( \frac{327080574378489058186401362669391}{32} a^{2} + \frac{751327153038248423223716642342565}{32} a - \frac{396813559161081723752766361904613}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -\frac{61630797877}{2} a^{2} - \frac{141570290417}{2} a + 74770372115\) , \( -8333010732273010 a^{2} - 19141513498967364 a + 20219186990752763\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-\frac{61630797877}{2}a^{2}-\frac{141570290417}{2}a+74770372115\right){x}-8333010732273010a^{2}-19141513498967364a+20219186990752763$ |
| 8.1-c8 |
8.1-c |
$8$ |
$28$ |
3.3.961.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.91756$ |
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2^{2} \) |
$1$ |
$0.065966108$ |
5.109181533 |
\( -\frac{269601931854184370352529501252989}{16} a^{2} + \frac{28739321262152343916935930708201}{8} a + 171327726175491275851667108507967 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -79956708197947603 a^{2} - 183666199225755010 a + 194006666517082295\) , \( -34828092759362198808763740 a^{2} - 80002585993882752368663130 a + 84506757840301284926749611\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-79956708197947603a^{2}-183666199225755010a+194006666517082295\right){x}-34828092759362198808763740a^{2}-80002585993882752368663130a+84506757840301284926749611$ |
*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.
