| 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 |
| 3.1-a1 |
3.1-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$11.06997$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$116.2296904$ |
2.152678528 |
\( \frac{63791259979876622}{531441} a^{3} + \frac{40426016608642742}{531441} a^{2} - \frac{148694095429555436}{531441} a - \frac{72662822899947101}{531441} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 5 a - 1\) , \( 4 a^{3} - 6 a^{2} - 14 a + 1\) , \( 27 a^{3} - 16 a^{2} - 128 a - 49\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(4a^{3}-6a^{2}-14a+1\right){x}+27a^{3}-16a^{2}-128a-49$ |
| 3.1-a2 |
3.1-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$11.06997$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$464.9187616$ |
2.152678528 |
\( -\frac{64986344}{729} a^{3} - \frac{40985144}{729} a^{2} + \frac{153470132}{729} a + \frac{77142629}{729} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} - 5 a - 1\) , \( -a^{3} - a^{2} + 6 a + 6\) , \( -a^{3} + 5 a + 3\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{3}-a^{2}+6a+6\right){x}-a^{3}+5a+3$ |
| 3.1-a3 |
3.1-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$11.06997$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$464.9187616$ |
2.152678528 |
\( \frac{5609257}{9} a^{3} - \frac{15326453}{9} a^{2} - \frac{13918606}{9} a + \frac{40495973}{9} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} - 5 a - 2\) , \( 8 a^{3} - 31 a^{2} + 18 a + 16\) , \( -40 a^{3} + 147 a^{2} - 82 a - 76\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(8a^{3}-31a^{2}+18a+16\right){x}-40a^{3}+147a^{2}-82a-76$ |
| 3.1-a4 |
3.1-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$11.06997$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$116.2296904$ |
2.152678528 |
\( -\frac{3383788332109}{81} a^{3} + \frac{2705242125866}{81} a^{2} + \frac{14167293434752}{81} a + \frac{5740179127237}{81} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -11 a^{3} + 24 a^{2} + 32 a - 63\) , \( -63 a^{3} + 138 a^{2} + 174 a - 355\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-11a^{3}+24a^{2}+32a-63\right){x}-63a^{3}+138a^{2}+174a-355$ |
| 3.1-b1 |
3.1-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$11.06997$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.120621869$ |
$1591.293134$ |
1.184996554 |
\( -\frac{64986344}{729} a^{3} - \frac{40985144}{729} a^{2} + \frac{153470132}{729} a + \frac{77142629}{729} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 32 a^{3} - 18 a^{2} - 153 a - 62\) , \( -207 a^{3} + 109 a^{2} + 987 a + 419\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(32a^{3}-18a^{2}-153a-62\right){x}-207a^{3}+109a^{2}+987a+419$ |
| 3.1-b2 |
3.1-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$11.06997$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.241243738$ |
$397.8232835$ |
1.184996554 |
\( \frac{63791259979876622}{531441} a^{3} + \frac{40426016608642742}{531441} a^{2} - \frac{148694095429555436}{531441} a - \frac{72662822899947101}{531441} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 3\) , \( a^{2} - 2\) , \( 21 a^{3} - 68 a^{2} + 8 a + 70\) , \( 75 a^{3} - 257 a^{2} + 81 a + 197\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(21a^{3}-68a^{2}+8a+70\right){x}+75a^{3}-257a^{2}+81a+197$ |
| 3.1-b3 |
3.1-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$11.06997$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.723731216$ |
$44.20258706$ |
1.184996554 |
\( -\frac{3383788332109}{81} a^{3} + \frac{2705242125866}{81} a^{2} + \frac{14167293434752}{81} a + \frac{5740179127237}{81} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - 5 a - 2\) , \( -44 a^{3} - 37 a^{2} + 91 a + 55\) , \( 537 a^{3} + 334 a^{2} - 1266 a - 619\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+3\right){x}^{2}+\left(-44a^{3}-37a^{2}+91a+55\right){x}+537a^{3}+334a^{2}-1266a-619$ |
| 3.1-b4 |
3.1-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$11.06997$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.361865608$ |
$176.8103482$ |
1.184996554 |
\( \frac{5609257}{9} a^{3} - \frac{15326453}{9} a^{2} - \frac{13918606}{9} a + \frac{40495973}{9} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( 0\) , \( a^{2} - 2\) , \( 3 a^{3} - 4 a^{2} - 10 a + 3\) , \( 7 a^{3} - a^{2} - 24 a - 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(3a^{3}-4a^{2}-10a+3\right){x}+7a^{3}-a^{2}-24a-10$ |
| 3.3-a1 |
3.3-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( 3^{2} \) |
$11.06997$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$464.9187616$ |
2.152678528 |
\( -\frac{5609257}{9} a^{3} + \frac{1501318}{9} a^{2} + \frac{27743741}{9} a + \frac{5620057}{3} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - a - 2\) , \( -7 a^{3} + 21 a^{2} + 18 a - 56\) , \( -46 a^{3} + 116 a^{2} + 130 a - 299\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-7a^{3}+21a^{2}+18a-56\right){x}-46a^{3}+116a^{2}+130a-299$ |
| 3.3-a2 |
3.3-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( - 3^{4} \) |
$11.06997$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$116.2296904$ |
2.152678528 |
\( \frac{3383788332109}{81} a^{3} - \frac{7446122870461}{81} a^{2} - \frac{9426412690157}{81} a + \frac{6409642118582}{27} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 12 a^{3} - 14 a^{2} - 45 a - 8\) , \( 63 a^{3} - 40 a^{2} - 286 a - 125\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-4\right){x}^{2}+\left(12a^{3}-14a^{2}-45a-8\right){x}+63a^{3}-40a^{2}-286a-125$ |
| 3.3-a3 |
3.3-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( - 3^{12} \) |
$11.06997$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$116.2296904$ |
2.152678528 |
\( -\frac{63791259979876622}{531441} a^{3} + \frac{231799796548272608}{531441} a^{2} - \frac{123531717727359914}{531441} a - \frac{39046547246994391}{177147} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( 0\) , \( -4 a^{3} + 8 a^{2} + 12 a - 20\) , \( -23 a^{3} + 58 a^{2} + 66 a - 148\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(-4a^{3}+8a^{2}+12a-20\right){x}-23a^{3}+58a^{2}+66a-148$ |
| 3.3-a4 |
3.3-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( 3^{6} \) |
$11.06997$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$464.9187616$ |
2.152678528 |
\( \frac{64986344}{729} a^{3} - \frac{235944176}{729} a^{2} + \frac{123459188}{729} a + \frac{41547091}{243} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( 0\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(a^{3}-2a^{2}-3a+5\right){x}$ |
| 3.3-b1 |
3.3-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( - 3^{12} \) |
$11.06997$ |
$(a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.241243738$ |
$397.8232835$ |
1.184996554 |
\( -\frac{63791259979876622}{531441} a^{3} + \frac{231799796548272608}{531441} a^{2} - \frac{123531717727359914}{531441} a - \frac{39046547246994391}{177147} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( 0\) , \( -20 a^{3} - 4 a^{2} + 64 a + 28\) , \( -121 a^{3} - 49 a^{2} + 339 a + 157\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(-20a^{3}-4a^{2}+64a+28\right){x}-121a^{3}-49a^{2}+339a+157$ |
| 3.3-b2 |
3.3-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( - 3^{4} \) |
$11.06997$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.723731216$ |
$44.20258706$ |
1.184996554 |
\( \frac{3383788332109}{81} a^{3} - \frac{7446122870461}{81} a^{2} - \frac{9426412690157}{81} a + \frac{6409642118582}{27} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 3\) , \( 45 a^{3} - 174 a^{2} + 115 a + 82\) , \( -491 a^{3} + 1770 a^{2} - 903 a - 929\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(45a^{3}-174a^{2}+115a+82\right){x}-491a^{3}+1770a^{2}-903a-929$ |
| 3.3-b3 |
3.3-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( 3^{2} \) |
$11.06997$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.361865608$ |
$176.8103482$ |
1.184996554 |
\( -\frac{5609257}{9} a^{3} + \frac{1501318}{9} a^{2} + \frac{27743741}{9} a + \frac{5620057}{3} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 2\) , \( -206 a^{3} + 525 a^{2} + 583 a - 1347\) , \( -3045 a^{3} + 7562 a^{2} + 8619 a - 19380\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(-206a^{3}+525a^{2}+583a-1347\right){x}-3045a^{3}+7562a^{2}+8619a-19380$ |
| 3.3-b4 |
3.3-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
3.3 |
\( 3 \) |
\( 3^{6} \) |
$11.06997$ |
$(a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.120621869$ |
$1591.293134$ |
1.184996554 |
\( \frac{64986344}{729} a^{3} - \frac{235944176}{729} a^{2} + \frac{123459188}{729} a + \frac{41547091}{243} \) |
\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - 4 a - 1\) , \( -34 a^{3} + 80 a^{2} + 97 a - 201\) , \( 206 a^{3} - 511 a^{2} - 584 a + 1308\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-3\right){x}^{2}+\left(-34a^{3}+80a^{2}+97a-201\right){x}+206a^{3}-511a^{2}-584a+1308$ |
| 9.5-a1 |
9.5-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.380677911$ |
$480.5308381$ |
3.387981572 |
\( -1462074 a^{3} + 769538 a^{2} + 6983107 a + 2979878 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( a\) , \( -5 a^{3} + 18 a^{2} - 13 a - 1\) , \( 24 a^{3} - 86 a^{2} + 43 a + 45\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(-5a^{3}+18a^{2}-13a-1\right){x}+24a^{3}-86a^{2}+43a+45$ |
| 9.5-a2 |
9.5-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.761355822$ |
$240.2654190$ |
3.387981572 |
\( -15005192749050 a^{3} + 7903917637613 a^{2} + 71665253548030 a + 30555194589977 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( a\) , \( 35 a^{3} - 132 a^{2} + 77 a + 64\) , \( 261 a^{3} - 948 a^{2} + 504 a + 479\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(35a^{3}-132a^{2}+77a+64\right){x}+261a^{3}-948a^{2}+504a+479$ |
| 9.5-a3 |
9.5-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.253785274$ |
$720.7962572$ |
3.387981572 |
\( 15005192749050 a^{3} - 37111660609537 a^{2} - 42457510576106 a + 95119173026570 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( 0\) , \( -4 a - 8\) , \( 8 a^{3} - 11 a^{2} - 41 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-4a-8\right){x}+8a^{3}-11a^{2}-41a-1$ |
| 9.5-a4 |
9.5-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.126892637$ |
$1441.592514$ |
3.387981572 |
\( 1462074 a^{3} - 3616684 a^{2} - 4135961 a + 9270449 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(a+2\right){x}$ |
| 9.5-b1 |
9.5-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.230891539$ |
$388.9004296$ |
1.663062382 |
\( 15005192749050 a^{3} - 37111660609537 a^{2} - 42457510576106 a + 95119173026570 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -19 a^{3} + 48 a^{2} + 72 a - 157\) , \( 132 a^{3} - 335 a^{2} - 316 a + 768\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-19a^{3}+48a^{2}+72a-157\right){x}+132a^{3}-335a^{2}-316a+768$ |
| 9.5-b2 |
9.5-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.115445769$ |
$777.8008592$ |
1.663062382 |
\( 1462074 a^{3} - 3616684 a^{2} - 4135961 a + 9270449 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} + 3 a^{2} - 3 a - 12\) , \( 3 a^{3} - 2 a^{2} - 7 a + 3\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(a^{3}+3a^{2}-3a-12\right){x}+3a^{3}-2a^{2}-7a+3$ |
| 9.5-b3 |
9.5-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.346337309$ |
$259.2669530$ |
1.663062382 |
\( -1462074 a^{3} + 769538 a^{2} + 6983107 a + 2979878 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2 a^{3} + 2 a^{2} + 4 a - 2\) , \( -4 a^{3} - a^{2} + 7 a + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-2a^{3}+2a^{2}+4a-2\right){x}-4a^{3}-a^{2}+7a+2$ |
| 9.5-b4 |
9.5-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.5 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.692674618$ |
$129.6334765$ |
1.663062382 |
\( -15005192749050 a^{3} + 7903917637613 a^{2} + 71665253548030 a + 30555194589977 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -17 a^{3} - 13 a^{2} + 44 a + 18\) , \( -144 a^{3} - 90 a^{2} + 334 a + 162\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-17a^{3}-13a^{2}+44a+18\right){x}-144a^{3}-90a^{2}+334a+162$ |
| 9.6-a1 |
9.6-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.380677911$ |
$480.5308381$ |
3.387981572 |
\( 1462074 a^{3} - 3616684 a^{2} - 4135961 a + 9270449 \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 6 a - 3\) , \( a^{3} - 5 a - 2\) , \( 3 a^{3} + 5 a^{2} - a\) , \( -15 a^{3} - 14 a^{2} + 26 a + 14\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-6a-3\right){x}^{2}+\left(3a^{3}+5a^{2}-a\right){x}-15a^{3}-14a^{2}+26a+14$ |
| 9.6-a2 |
9.6-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.761355822$ |
$240.2654190$ |
3.387981572 |
\( 15005192749050 a^{3} - 37111660609537 a^{2} - 42457510576106 a + 95119173026570 \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 6 a - 3\) , \( a^{3} - 5 a - 2\) , \( -37 a^{3} - 25 a^{2} + 89 a + 45\) , \( -297 a^{3} - 180 a^{2} + 708 a + 344\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}-5a-2\right){y}={x}^{3}+\left(a^{3}-6a-3\right){x}^{2}+\left(-37a^{3}-25a^{2}+89a+45\right){x}-297a^{3}-180a^{2}+708a+344$ |
| 9.6-a3 |
9.6-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.253785274$ |
$720.7962572$ |
3.387981572 |
\( -15005192749050 a^{3} + 7903917637613 a^{2} + 71665253548030 a + 30555194589977 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 5 a - 1\) , \( 3 a^{3} - 2 a^{2} - 5 a - 10\) , \( -5 a^{3} + 17 a^{2} + 22 a - 60\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+5\right){x}^{2}+\left(3a^{3}-2a^{2}-5a-10\right){x}-5a^{3}+17a^{2}+22a-60$ |
| 9.6-a4 |
9.6-a |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.126892637$ |
$1441.592514$ |
3.387981572 |
\( -1462074 a^{3} + 769538 a^{2} + 6983107 a + 2979878 \) |
\( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 5 a - 1\) , \( 3 a^{3} - 2 a^{2} - 10 a + 5\) , \( 3 a^{3} - a^{2} - 7 a\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+5\right){x}^{2}+\left(3a^{3}-2a^{2}-10a+5\right){x}+3a^{3}-a^{2}-7a$ |
| 9.6-b1 |
9.6-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.346337309$ |
$259.2669530$ |
1.663062382 |
\( 1462074 a^{3} - 3616684 a^{2} - 4135961 a + 9270449 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{3} - 4 a - 1\) , \( 3 a^{3} - 5 a^{2} - 3 a + 7\) , \( 5 a^{3} - 6 a^{2} - 2\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(3a^{3}-5a^{2}-3a+7\right){x}+5a^{3}-6a^{2}-2$ |
| 9.6-b2 |
9.6-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.692674618$ |
$129.6334765$ |
1.663062382 |
\( 15005192749050 a^{3} - 37111660609537 a^{2} - 42457510576106 a + 95119173026570 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{3} - 4 a - 1\) , \( 18 a^{3} - 65 a^{2} + 32 a + 37\) , \( 115 a^{3} - 420 a^{2} + 226 a + 211\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(18a^{3}-65a^{2}+32a+37\right){x}+115a^{3}-420a^{2}+226a+211$ |
| 9.6-b3 |
9.6-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.230891539$ |
$388.9004296$ |
1.663062382 |
\( -15005192749050 a^{3} + 7903917637613 a^{2} + 71665253548030 a + 30555194589977 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{3} - 4 a - 2\) , \( 22 a^{3} - 18 a^{2} - 115 a - 44\) , \( -125 a^{3} + 44 a^{2} + 550 a + 236\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(22a^{3}-18a^{2}-115a-44\right){x}-125a^{3}+44a^{2}+550a+236$ |
| 9.6-b4 |
9.6-b |
$4$ |
$6$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
9.6 |
\( 3^{2} \) |
\( 3^{6} \) |
$12.69950$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.115445769$ |
$777.8008592$ |
1.663062382 |
\( -1462074 a^{3} + 769538 a^{2} + 6983107 a + 2979878 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{3} - 4 a - 2\) , \( 2 a^{3} - 3 a^{2} - 10 a + 1\) , \( -a^{3} + 2 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-4a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(2a^{3}-3a^{2}-10a+1\right){x}-a^{3}+2a-1$ |
| 16.1-a1 |
16.1-a |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.2 |
$1$ |
\( 5 \) |
$13.70852253$ |
$1.732309876$ |
4.398233981 |
\( \frac{1250637664527933}{32} a^{2} - \frac{1250637664527933}{32} a - \frac{2690606637259811}{16} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 2\) , \( 276 a^{3} - 49 a^{2} - 1117 a - 490\) , \( 4561 a^{3} - 1515 a^{2} - 19915 a - 8606\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(276a^{3}-49a^{2}-1117a-490\right){x}+4561a^{3}-1515a^{2}-19915a-8606$ |
| 16.1-a2 |
16.1-a |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1 |
$1$ |
\( 1 \) |
$2.741704506$ |
$43.30774691$ |
4.398233981 |
\( -\frac{461373}{2} a^{2} + \frac{461373}{2} a + \frac{321323}{2} \) |
\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - 4 a - 3\) , \( a + 1\) , \( 11 a^{3} - 41 a^{2} + 27 a + 22\) , \( 60 a^{3} - 215 a^{2} + 113 a + 105\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}^{2}+\left(11a^{3}-41a^{2}+27a+22\right){x}+60a^{3}-215a^{2}+113a+105$ |
| 16.1-a3 |
16.1-a |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 1 \) |
$0.304633834$ |
$3507.927500$ |
4.398233981 |
\( \frac{461373}{2} a^{2} - \frac{461373}{2} a - 992771 \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - 4 a - 1\) , \( 10 a^{3} - 6 a^{2} - 49 a - 20\) , \( -9 a^{3} + 4 a^{2} + 42 a + 18\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(10a^{3}-6a^{2}-49a-20\right){x}-9a^{3}+4a^{2}+42a+18$ |
| 16.1-a4 |
16.1-a |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 5 \) |
$1.523169170$ |
$140.3171000$ |
4.398233981 |
\( -\frac{1250637664527933}{32} a^{2} + \frac{1250637664527933}{32} a + \frac{871975048120043}{32} \) |
\( \bigl[a^{3} - 5 a - 2\) , \( -a^{2} + 2 a + 3\) , \( a^{3} - 4 a - 1\) , \( -265 a^{3} - 21 a^{2} + 931 a + 420\) , \( 2499 a^{3} + 1297 a^{2} - 6430 a - 3068\bigr] \) |
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-265a^{3}-21a^{2}+931a+420\right){x}+2499a^{3}+1297a^{2}-6430a-3068$ |
| 16.1-a5 |
16.1-a |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs.1.1, 5B.4.1 |
$1$ |
\( 3 \) |
$0.913901502$ |
$389.7697222$ |
4.398233981 |
\( \frac{1331}{8} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( 0\) , \( a^{3} - 5 a - 1\) , \( 8 a^{3} + 4 a^{2} - 20 a - 10\) , \( -33 a^{3} - 22 a^{2} + 76 a + 37\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(8a^{3}+4a^{2}-20a-10\right){x}-33a^{3}-22a^{2}+76a+37$ |
| 16.1-a6 |
16.1-a |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs.1.1, 5B.4.2 |
$1$ |
\( 3 \cdot 5 \) |
$4.569507510$ |
$15.59078888$ |
4.398233981 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( 0\) , \( a^{3} - 5 a - 1\) , \( -567 a^{3} - 371 a^{2} + 1305 a + 640\) , \( 19146 a^{3} + 12102 a^{2} - 44700 a - 21836\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-567a^{3}-371a^{2}+1305a+640\right){x}+19146a^{3}+12102a^{2}-44700a-21836$ |
| 16.1-b1 |
16.1-b |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.1 |
$1$ |
\( 3 \) |
$0.365902225$ |
$815.4744629$ |
1.326321337 |
\( \frac{1331}{8} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( -a^{2} + a + 3\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}+a+3\right){x}-a^{2}+a+3$ |
| 16.1-b2 |
16.1-b |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.2 |
$1$ |
\( 3 \cdot 5 \) |
$1.829511129$ |
$1.304759140$ |
1.326321337 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - a - 2\) , \( 74 a^{2} - 74 a - 322\) , \( 432 a^{2} - 432 a - 1862\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(74a^{2}-74a-322\right){x}+432a^{2}-432a-1862$ |
| 16.1-b3 |
16.1-b |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 5 \) |
$5.488533388$ |
$1.304759140$ |
1.326321337 |
\( \frac{1250637664527933}{32} a^{2} - \frac{1250637664527933}{32} a - \frac{2690606637259811}{16} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - a - 3\) , \( 28 a^{2} - 28 a - 82\) , \( 52 a^{2} - 52 a - 262\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+{x}^{2}+\left(28a^{2}-28a-82\right){x}+52a^{2}-52a-262$ |
| 16.1-b4 |
16.1-b |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1.097706677$ |
$815.4744629$ |
1.326321337 |
\( -\frac{461373}{2} a^{2} + \frac{461373}{2} a + \frac{321323}{2} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - a - 3\) , \( -2 a^{2} + 2 a + 3\) , \( a^{2} - a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+{x}^{2}+\left(-2a^{2}+2a+3\right){x}+a^{2}-a-2$ |
| 16.1-b5 |
16.1-b |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1.097706677$ |
$815.4744629$ |
1.326321337 |
\( \frac{461373}{2} a^{2} - \frac{461373}{2} a - 992771 \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 5\) , \( -a^{2} + a + 3\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+{x}^{2}+\left(a^{2}-a-5\right){x}-a^{2}+a+3$ |
| 16.1-b6 |
16.1-b |
$6$ |
$45$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$13.64651$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 5 \) |
$5.488533388$ |
$1.304759140$ |
1.326321337 |
\( -\frac{1250637664527933}{32} a^{2} + \frac{1250637664527933}{32} a + \frac{871975048120043}{32} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - a - 2\) , \( -29 a^{2} + 29 a + 60\) , \( -52 a^{2} + 52 a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+{x}^{2}+\left(-29a^{2}+29a+60\right){x}-52a^{2}+52a-2$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$14.27981$ |
$(a^3-3a^2-a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.018540778$ |
$1653.776834$ |
2.271574402 |
\( -\frac{156803}{23} a^{2} + \frac{156803}{23} a + \frac{262930}{23} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a + 1\) , \( -3 a^{3} + 9 a + 4\) , \( 5 a^{3} - 2 a^{2} - 23 a - 10\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-3a^{3}+9a+4\right){x}+5a^{3}-2a^{2}-23a-10$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{4} \) |
$14.27981$ |
$(a^3-3a^2-a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.074163115$ |
$413.4442086$ |
2.271574402 |
\( \frac{50955500525}{529} a^{2} - \frac{50955500525}{529} a - \frac{35527249741}{529} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a + 1\) , \( 41 a^{3} - 144 a^{2} + 64 a + 89\) , \( -356 a^{3} + 1287 a^{2} - 652 a - 696\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(41a^{3}-144a^{2}+64a+89\right){x}-356a^{3}+1287a^{2}-652a-696$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$14.27981$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$168.8175776$ |
3.126653553 |
\( -\frac{156803}{23} a^{2} + \frac{156803}{23} a + \frac{262930}{23} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 0\) , \( a^{2} - a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(a^{2}-a-1\right){x}$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{4} \) |
$14.27981$ |
$(a^3-3a^2-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$42.20439440$ |
3.126653553 |
\( \frac{50955500525}{529} a^{2} - \frac{50955500525}{529} a - \frac{35527249741}{529} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 0\) , \( -4 a^{2} + 4 a + 4\) , \( -13 a^{2} + 13 a + 8\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-4a^{2}+4a+4\right){x}-13a^{2}+13a+8$ |
| 25.1-a1 |
25.1-a |
$3$ |
$9$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$14.42942$ |
$(-a^3+2a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$29.88504742$ |
2.490740950 |
\( -\frac{78903093985421}{5} a^{3} + \frac{195127722929294}{5} a^{2} + \frac{223338994328504}{5} a - \frac{500249924836657}{5} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a - 1\) , \( -24 a^{3} + 55 a^{2} + 52 a - 172\) , \( -121 a^{3} + 380 a^{2} + 289 a - 1068\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-24a^{3}+55a^{2}+52a-172\right){x}-121a^{3}+380a^{2}+289a-1068$ |
| 25.1-a2 |
25.1-a |
$3$ |
$9$ |
4.4.11661.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$14.42942$ |
$(-a^3+2a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$268.9654268$ |
2.490740950 |
\( -\frac{798514}{125} a^{3} + \frac{2005166}{125} a^{2} + \frac{2387086}{125} a - \frac{5314873}{125} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 4 a - 1\) , \( a^{3} - 3 a - 2\) , \( a^{2} - 3\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(a^{3}-3a-2\right){x}+a^{2}-3$ |
*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.
