| 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 |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{10} \) |
$8.05385$ |
$(a^2+a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2089.629091$ |
1.102864053 |
\( -\frac{7891043}{8} a^{3} + \frac{2963693}{4} a^{2} + 4376076 a - \frac{10508429}{8} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -1\) , \( -a^{3} + a^{2} + 4 a\) , \( -3 a^{3} + 2 a^{2} + 13 a - 4\) , \( a^{3} - a^{2} - 4 a + 1\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+\left(-a^{3}+a^{2}+4a\right){y}={x}^{3}-{x}^{2}+\left(-3a^{3}+2a^{2}+13a-4\right){x}+a^{3}-a^{2}-4a+1$ |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{50} \) |
$8.05385$ |
$(a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$3.343406546$ |
1.102864053 |
\( \frac{2247102641020357}{8192} a^{3} + \frac{5347830388779643}{8192} a^{2} + \frac{1491671351335715}{8192} a - \frac{472104570059161}{4096} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -1\) , \( -a^{3} + a^{2} + 4 a\) , \( 17 a^{3} - 18 a^{2} - 87 a + 11\) , \( 5 a^{3} - 28 a^{2} - 62 a - 3\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+\left(-a^{3}+a^{2}+4a\right){y}={x}^{3}-{x}^{2}+\left(17a^{3}-18a^{2}-87a+11\right){x}+5a^{3}-28a^{2}-62a-3$ |
| 4.1-b1 |
4.1-b |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{10} \) |
$8.05385$ |
$(a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.004737856$ |
$1067.892631$ |
1.335156876 |
\( -\frac{7891043}{8} a^{3} + \frac{2963693}{4} a^{2} + 4376076 a - \frac{10508429}{8} \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( a^{3} - 5 a - 1\) , \( 2 a^{2} - a - 1\) , \( -a^{3} + 4 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(2a^{2}-a-1\right){x}-a^{3}+4a^{2}-4$ |
| 4.1-b2 |
4.1-b |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{50} \) |
$8.05385$ |
$(a^2+a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5^{2} \) |
$0.023689283$ |
$42.71570524$ |
1.335156876 |
\( \frac{2247102641020357}{8192} a^{3} + \frac{5347830388779643}{8192} a^{2} + \frac{1491671351335715}{8192} a - \frac{472104570059161}{4096} \) |
\( \bigl[a + 1\) , \( -2 a^{3} + a^{2} + 9 a - 1\) , \( -a^{3} + a^{2} + 5 a\) , \( 62 a^{3} - 79 a^{2} - 175 a + 22\) , \( 511 a^{3} - 1071 a^{2} - 466 a + 283\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+9a-1\right){x}^{2}+\left(62a^{3}-79a^{2}-175a+22\right){x}+511a^{3}-1071a^{2}-466a+283$ |
| 16.1-a1 |
16.1-a |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$159.3897851$ |
1.577300833 |
\( 12652032 a^{3} - 9503488 a^{2} - 56128512 a + 16848384 \) |
\( \bigl[0\) , \( -a^{3} + 4 a\) , \( 0\) , \( 4 a^{3} - 7 a^{2} - 6 a + 3\) , \( -8 a^{3} + 15 a^{2} + 11 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(4a^{3}-7a^{2}-6a+3\right){x}-8a^{3}+15a^{2}+11a-4$ |
| 16.1-a2 |
16.1-a |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$637.5591405$ |
1.577300833 |
\( -35026491440492 a^{3} + 67258593314288 a^{2} + 45981100753252 a - 18240854228472 \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{2} + a + 1\) , \( a^{2} - a - 1\) , \( -35 a^{3} + 27 a^{2} + 158 a - 62\) , \( 138 a^{3} - 101 a^{2} - 628 a + 204\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-35a^{3}+27a^{2}+158a-62\right){x}+138a^{3}-101a^{2}-628a+204$ |
| 16.1-a3 |
16.1-a |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 3 \) |
$1$ |
$637.5591405$ |
1.577300833 |
\( 9914144 a^{3} + 31222448 a^{2} + 10084448 a - 5829552 \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{2} + a + 1\) , \( a^{2} - a - 1\) , \( -10 a^{3} + 7 a^{2} + 43 a - 12\) , \( -25 a^{3} + 18 a^{2} + 112 a - 34\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-10a^{3}+7a^{2}+43a-12\right){x}-25a^{3}+18a^{2}+112a-34$ |
| 16.1-a4 |
16.1-a |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 3 \) |
$1$ |
$39.84744628$ |
1.577300833 |
\( 3841162954703212 a^{3} + 9141499684257040 a^{2} + 2549840339975836 a - 1614016666205240 \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{2} + a + 1\) , \( a^{2} - a - 1\) , \( 15 a^{3} - 13 a^{2} - 72 a + 18\) , \( -98 a^{3} + 69 a^{2} + 426 a - 136\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(15a^{3}-13a^{2}-72a+18\right){x}-98a^{3}+69a^{2}+426a-136$ |
| 16.1-b1 |
16.1-b |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$379.5098122$ |
1.251860113 |
\( -35026491440492 a^{3} + 67258593314288 a^{2} + 45981100753252 a - 18240854228472 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - a - 1\) , \( -a^{3} + a^{2} + 5 a\) , \( -39 a^{3} + 15 a^{2} + 144 a - 48\) , \( 144 a^{3} - 58 a^{2} - 562 a + 157\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-39a^{3}+15a^{2}+144a-48\right){x}+144a^{3}-58a^{2}-562a+157$ |
| 16.1-b2 |
16.1-b |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$379.5098122$ |
1.251860113 |
\( 3841162954703212 a^{3} + 9141499684257040 a^{2} + 2549840339975836 a - 1614016666205240 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 1\) , \( 9 a^{3} - 7 a^{2} - 38 a - 19\) , \( -17 a^{3} + 25 a^{2} + 45 a + 13\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(9a^{3}-7a^{2}-38a-19\right){x}-17a^{3}+25a^{2}+45a+13$ |
| 16.1-b3 |
16.1-b |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$1518.039249$ |
1.251860113 |
\( 9914144 a^{3} + 31222448 a^{2} + 10084448 a - 5829552 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 1\) , \( 4 a^{3} - 7 a^{2} - 8 a + 1\) , \( -9 a^{3} + 23 a^{2} + 2 a - 15\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(4a^{3}-7a^{2}-8a+1\right){x}-9a^{3}+23a^{2}+2a-15$ |
| 16.1-b4 |
16.1-b |
$4$ |
$4$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$9.57769$ |
$(a^2+a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$379.5098122$ |
1.251860113 |
\( 12652032 a^{3} - 9503488 a^{2} - 56128512 a + 16848384 \) |
\( \bigl[0\) , \( -2 a^{3} + a^{2} + 9 a + 1\) , \( 0\) , \( -8 a^{3} - 22 a^{2} - 8 a + 9\) , \( 50 a^{3} + 122 a^{2} + 39 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(-2a^{3}+a^{2}+9a+1\right){x}^{2}+\left(-8a^{3}-22a^{2}-8a+9\right){x}+50a^{3}+122a^{2}+39a-21$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$9.65055$ |
$(a^2-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$184.4286477$ |
2.433442935 |
\( -\frac{9280666137}{4913} a^{3} - \frac{68843781023}{4913} a^{2} - \frac{24295621869}{4913} a + \frac{16652449695}{4913} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -2 a^{3} + a^{2} + 8 a + 1\) , \( -a^{3} + a^{2} + 5 a\) , \( -3 a^{3} + a^{2} + 9 a\) , \( -11 a^{3} + 7 a^{2} + 45 a - 13\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(-a^{3}+a^{2}+5a\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+8a+1\right){x}^{2}+\left(-3a^{3}+a^{2}+9a\right){x}-11a^{3}+7a^{2}+45a-13$ |
| 17.1-b1 |
17.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$9.65055$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$307.8024718$ |
2.030649141 |
\( -\frac{2712300915302597}{24137569} a^{3} - \frac{861583963356942}{24137569} a^{2} + \frac{13363979345271242}{24137569} a + \frac{9634906213427192}{24137569} \) |
\( \bigl[a^{2} - 1\) , \( 2 a^{3} - a^{2} - 9 a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 14 a^{3} - 2 a^{2} - 62 a - 27\) , \( 21 a^{3} + 5 a^{2} - 106 a - 67\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(-a^{3}+a^{2}+4a-1\right){y}={x}^{3}+\left(2a^{3}-a^{2}-9a+1\right){x}^{2}+\left(14a^{3}-2a^{2}-62a-27\right){x}+21a^{3}+5a^{2}-106a-67$ |
| 17.1-b2 |
17.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$9.65055$ |
$(a^2-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$615.6049437$ |
2.030649141 |
\( \frac{110962134}{4913} a^{3} + \frac{199269684}{4913} a^{2} - \frac{82968178}{4913} a - \frac{107581645}{4913} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 1\) , \( a^{3} - 5 a - 1\) , \( -3 a^{3} + 4 a^{2} + 12 a - 3\) , \( a^{3} + a^{2} - 6 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-3a^{3}+4a^{2}+12a-3\right){x}+a^{3}+a^{2}-6a$ |
| 17.1-c1 |
17.1-c |
$2$ |
$3$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$9.65055$ |
$(a^2-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$12.20518653$ |
1.449371493 |
\( -\frac{5046977834405570395}{4913} a^{3} - \frac{1470522239949015371}{4913} a^{2} + \frac{24806427686194829270}{4913} a + \frac{17321727365860720482}{4913} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( a^{3} - 6 a - 1\) , \( a^{3} - 5 a - 1\) , \( 46 a^{3} - 207 a - 127\) , \( 207 a^{3} - 3 a^{2} - 915 a - 596\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(46a^{3}-207a-127\right){x}+207a^{3}-3a^{2}-915a-596$ |
| 17.1-c2 |
17.1-c |
$2$ |
$3$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$9.65055$ |
$(a^2-2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$988.6201097$ |
1.449371493 |
\( -\frac{608242}{17} a^{3} - \frac{179684}{17} a^{2} + \frac{2976663}{17} a + \frac{2072127}{17} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( a^{3} - 6 a - 1\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 7 a + 3\) , \( a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(a^{3}-7a+3\right){x}+a^{2}-2a-1$ |
| 17.1-d1 |
17.1-d |
$2$ |
$3$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( -17 \) |
$9.65055$ |
$(a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.051991874$ |
$713.0293279$ |
1.956571160 |
\( -\frac{608242}{17} a^{3} - \frac{179684}{17} a^{2} + \frac{2976663}{17} a + \frac{2072127}{17} \) |
\( \bigl[1\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 5 a\) , \( -8 a^{3} + 5 a^{2} + 36 a - 7\) , \( 28 a^{3} - 21 a^{2} - 124 a + 36\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-8a^{3}+5a^{2}+36a-7\right){x}+28a^{3}-21a^{2}-124a+36$ |
| 17.1-d2 |
17.1-d |
$2$ |
$3$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$9.65055$ |
$(a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.155975624$ |
$79.22548087$ |
1.956571160 |
\( -\frac{5046977834405570395}{4913} a^{3} - \frac{1470522239949015371}{4913} a^{2} + \frac{24806427686194829270}{4913} a + \frac{17321727365860720482}{4913} \) |
\( \bigl[1\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 5 a\) , \( 67 a^{3} - 45 a^{2} - 299 a + 63\) , \( -699 a^{3} + 504 a^{2} + 3111 a - 837\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(67a^{3}-45a^{2}-299a+63\right){x}-699a^{3}+504a^{2}+3111a-837$ |
| 17.1-e1 |
17.1-e |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{6} \) |
$9.65055$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.022379274$ |
$948.8047725$ |
1.680996848 |
\( -\frac{2712300915302597}{24137569} a^{3} - \frac{861583963356942}{24137569} a^{2} + \frac{13363979345271242}{24137569} a + \frac{9634906213427192}{24137569} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{2} + 3\) , \( a^{3} - 5 a\) , \( -23 a^{3} + 17 a^{2} + 100 a - 34\) , \( 58 a^{3} - 44 a^{2} - 257 a + 78\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-23a^{3}+17a^{2}+100a-34\right){x}+58a^{3}-44a^{2}-257a+78$ |
| 17.1-e2 |
17.1-e |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$9.65055$ |
$(a^2-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$0.044758549$ |
$948.8047725$ |
1.680996848 |
\( \frac{110962134}{4913} a^{3} + \frac{199269684}{4913} a^{2} - \frac{82968178}{4913} a - \frac{107581645}{4913} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{2} + 3\) , \( a^{3} - 5 a\) , \( 2 a^{3} - 3 a^{2} - 10 a + 6\) , \( -a^{3} + 4 a - 1\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(2a^{3}-3a^{2}-10a+6\right){x}-a^{3}+4a-1$ |
| 17.1-f1 |
17.1-f |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{3} \) |
$9.65055$ |
$(a^2-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.013859577$ |
$507.6259882$ |
1.113955591 |
\( -\frac{9280666137}{4913} a^{3} - \frac{68843781023}{4913} a^{2} - \frac{24295621869}{4913} a + \frac{16652449695}{4913} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 6 a\) , \( a^{3} - 5 a\) , \( 8 a^{3} - 12 a^{2} - 21 a + 1\) , \( -22 a^{3} + 47 a^{2} + 23 a - 23\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(8a^{3}-12a^{2}-21a+1\right){x}-22a^{3}+47a^{2}+23a-23$ |
| 19.1-a1 |
19.1-a |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$9.78566$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$719.2901554$ |
2.372667652 |
\( \frac{7249536}{19} a^{3} - \frac{1883712}{19} a^{2} - 2182144 a + \frac{12017024}{19} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -2 a^{3} + a^{2} + 9 a + 1\) , \( a^{3} - 5 a - 1\) , \( 3 a^{3} - 7 a^{2} - 2 a + 6\) , \( 9 a^{3} - 19 a^{2} - 8 a + 6\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-2a^{3}+a^{2}+9a+1\right){x}^{2}+\left(3a^{3}-7a^{2}-2a+6\right){x}+9a^{3}-19a^{2}-8a+6$ |
| 19.1-a2 |
19.1-a |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$9.78566$ |
$(a^3-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$359.6450777$ |
2.372667652 |
\( -\frac{669843712}{361} a^{3} - \frac{195041728}{361} a^{2} + \frac{173298176}{19} a + \frac{2298837824}{361} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a + 1\) , \( -12 a^{3} + 11 a^{2} + 47 a - 15\) , \( 58 a^{3} - 42 a^{2} - 262 a + 77\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-12a^{3}+11a^{2}+47a-15\right){x}+58a^{3}-42a^{2}-262a+77$ |
| 19.1-b1 |
19.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$9.78566$ |
$(a^3-5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.084068493$ |
$1162.416032$ |
1.289399926 |
\( \frac{7249536}{19} a^{3} - \frac{1883712}{19} a^{2} - 2182144 a + \frac{12017024}{19} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 5 a\) , \( a^{2} - 1\) , \( -2 a^{3} - 9 a^{2} - 6 a + 3\) , \( -10 a^{3} - 24 a^{2} - 6 a + 4\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-2a^{3}-9a^{2}-6a+3\right){x}-10a^{3}-24a^{2}-6a+4$ |
| 19.1-b2 |
19.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$9.78566$ |
$(a^3-5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.042034246$ |
$1162.416032$ |
1.289399926 |
\( -\frac{669843712}{361} a^{3} - \frac{195041728}{361} a^{2} + \frac{173298176}{19} a + \frac{2298837824}{361} \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} - 2\) , \( 2 a^{3} + a^{2} - 7 a - 6\) , \( -a^{3} + 8 a + 5\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(2a^{3}+a^{2}-7a-6\right){x}-a^{3}+8a+5$ |
| 20.1-a1 |
20.1-a |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{7} \) |
$9.84860$ |
$(a^3-5a-1), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$21.61881723$ |
1.996745684 |
\( -\frac{24518107396}{78125} a^{3} + \frac{18906189803}{156250} a^{2} + \frac{266352201283}{156250} a - \frac{79833089663}{156250} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 4 a + 1\) , \( a^{2} - a - 1\) , \( -2 a^{3} + a^{2} + 10 a - 4\) , \( -a^{3} + a^{2} + 6 a - 5\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-2a^{3}+a^{2}+10a-4\right){x}-a^{3}+a^{2}+6a-5$ |
| 20.1-b1 |
20.1-b |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5 \) |
$9.84860$ |
$(a^3-5a-1), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$3.739252675$ |
1.233438800 |
\( -\frac{1208466213499318406233}{5} a^{3} - \frac{5752007507947181906231}{10} a^{2} - \frac{1604409131539861406421}{10} a + \frac{1015570466863326226091}{10} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -142 a^{3} - 40 a^{2} + 465 a - 52\) , \( -214 a^{3} + 1549 a^{2} + 3424 a - 945\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-142a^{3}-40a^{2}+465a-52\right){x}-214a^{3}+1549a^{2}+3424a-945$ |
| 20.1-b2 |
20.1-b |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{5} \) |
$9.84860$ |
$(a^3-5a-1), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$93.48131688$ |
1.233438800 |
\( \frac{709649759}{6250} a^{3} + \frac{772622151}{25000} a^{2} - \frac{14055646439}{25000} a - \frac{9750211021}{25000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3 a^{3} - 15 a - 7\) , \( 2 a^{3} + a^{2} - 10 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a^{3}-15a-7\right){x}+2a^{3}+a^{2}-10a-9$ |
| 20.1-c1 |
20.1-c |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{5} \) |
$9.84860$ |
$(a^3-5a-1), (a^2+a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$122.8807596$ |
1.621349611 |
\( \frac{709649759}{6250} a^{3} + \frac{772622151}{25000} a^{2} - \frac{14055646439}{25000} a - \frac{9750211021}{25000} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -a^{2} + 2 a + 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 5 a^{3} - 22 a - 13\) , \( -3 a^{3} - 2 a^{2} + 17 a + 12\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(-a^{3}+a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(5a^{3}-22a-13\right){x}-3a^{3}-2a^{2}+17a+12$ |
| 20.1-c2 |
20.1-c |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5 \) |
$9.84860$ |
$(a^3-5a-1), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.196609215$ |
1.621349611 |
\( -\frac{1208466213499318406233}{5} a^{3} - \frac{5752007507947181906231}{10} a^{2} - \frac{1604409131539861406421}{10} a + \frac{1015570466863326226091}{10} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -a^{2} + 2 a + 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 190 a^{3} - 575 a^{2} + 223 a + 157\) , \( 6830 a^{3} - 13997 a^{2} - 6416 a + 2462\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(-a^{3}+a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(190a^{3}-575a^{2}+223a+157\right){x}+6830a^{3}-13997a^{2}-6416a+2462$ |
| 20.1-d1 |
20.1-d |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{7} \) |
$9.84860$ |
$(a^3-5a-1), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$54.08870876$ |
0.713673216 |
\( -\frac{24518107396}{78125} a^{3} + \frac{18906189803}{156250} a^{2} + \frac{266352201283}{156250} a - \frac{79833089663}{156250} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 1\) , \( a^{3} - 5 a - 1\) , \( 4 a^{3} - 2 a^{2} - 14 a - 8\) , \( -2 a^{3} - 3 a^{2} + 14 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(4a^{3}-2a^{2}-14a-8\right){x}-2a^{3}-3a^{2}+14a+10$ |
| 28.1-a1 |
28.1-a |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$10.27166$ |
$(a-2), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$154.3884332$ |
2.037077464 |
\( \frac{282851207775}{14} a^{3} - \frac{674933034371}{14} a^{2} - \frac{19253331919}{14} a + \frac{27955724868}{7} \) |
\( \bigl[a + 1\) , \( 2 a^{3} - a^{2} - 8 a + 1\) , \( 0\) , \( 13 a^{3} + 3 a^{2} - 59 a - 34\) , \( -37 a^{3} - 8 a^{2} + 184 a + 123\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a^{3}-a^{2}-8a+1\right){x}^{2}+\left(13a^{3}+3a^{2}-59a-34\right){x}-37a^{3}-8a^{2}+184a+123$ |
| 28.1-b1 |
28.1-b |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$10.27166$ |
$(a-2), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$3.206420587$ |
1.057677538 |
\( \frac{86476572820879899612471}{7} a^{3} - \frac{332105712502327830543747}{14} a^{2} - \frac{227048671772881064356059}{14} a + \frac{90064885064043512054195}{14} \) |
\( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( 2 a^{3} - a^{2} - 10 a + 1\) , \( a^{2} - a - 1\) , \( 1573 a^{3} + 3726 a^{2} + 1007 a - 680\) , \( 26047 a^{3} + 62700 a^{2} + 18507 a - 11267\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(2a^{3}-a^{2}-10a+1\right){x}^{2}+\left(1573a^{3}+3726a^{2}+1007a-680\right){x}+26047a^{3}+62700a^{2}+18507a-11267$ |
| 28.1-b2 |
28.1-b |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{10} \cdot 7^{5} \) |
$10.27166$ |
$(a-2), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$80.16051468$ |
1.057677538 |
\( -\frac{3393361847}{33614} a^{3} - \frac{34292637681}{134456} a^{2} - \frac{9875938341}{134456} a + \frac{5772735299}{134456} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( a^{3} - 6 a - 1\) , \( a^{2} - 2\) , \( a^{3} - 5 a^{2} + 4 a + 2\) , \( 16 a^{3} - 30 a^{2} - 24 a + 8\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(a^{3}-5a^{2}+4a+2\right){x}+16a^{3}-30a^{2}-24a+8$ |
| 28.1-c1 |
28.1-c |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$10.27166$ |
$(a-2), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.235748438$ |
1.944113543 |
\( \frac{86476572820879899612471}{7} a^{3} - \frac{332105712502327830543747}{14} a^{2} - \frac{227048671772881064356059}{14} a + \frac{90064885064043512054195}{14} \) |
\( \bigl[a + 1\) , \( a^{3} - 6 a - 1\) , \( 1\) , \( 71 a^{3} - 54 a^{2} - 85 a - 45\) , \( 333 a^{3} - 918 a^{2} + 158 a - 164\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(71a^{3}-54a^{2}-85a-45\right){x}+333a^{3}-918a^{2}+158a-164$ |
| 28.1-c2 |
28.1-c |
$2$ |
$5$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{10} \cdot 7^{5} \) |
$10.27166$ |
$(a-2), (a^2+a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$147.3427738$ |
1.944113543 |
\( -\frac{3393361847}{33614} a^{3} - \frac{34292637681}{134456} a^{2} - \frac{9875938341}{134456} a + \frac{5772735299}{134456} \) |
\( \bigl[a + 1\) , \( a^{3} - 6 a - 1\) , \( 1\) , \( -4 a^{3} - 4 a^{2} + 5 a\) , \( 7 a^{3} + 14 a^{2} - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-6a-1\right){x}^{2}+\left(-4a^{3}-4a^{2}+5a\right){x}+7a^{3}+14a^{2}-2$ |
| 28.1-d1 |
28.1-d |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$10.27166$ |
$(a-2), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$62.73286123$ |
0.827728445 |
\( \frac{282851207775}{14} a^{3} - \frac{674933034371}{14} a^{2} - \frac{19253331919}{14} a + \frac{27955724868}{7} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -a^{3} + 6 a\) , \( a^{3} - 4 a\) , \( 32 a^{3} - 10 a^{2} - 127 a - 75\) , \( 89 a^{3} + 110 a^{2} - 575 a - 458\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+6a\right){x}^{2}+\left(32a^{3}-10a^{2}-127a-75\right){x}+89a^{3}+110a^{2}-575a-458$ |
| 31.1-a1 |
31.1-a |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$10.40318$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$727.1710921$ |
2.398663898 |
\( -\frac{19049067382}{29791} a^{3} - \frac{5512270820}{29791} a^{2} + \frac{93644765890}{29791} a + \frac{65326096677}{29791} \) |
\( \bigl[a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - 8 a\) , \( a^{2} - a - 1\) , \( 6 a^{3} - 7 a^{2} - 16 a + 5\) , \( a^{3} - 3 a + 1\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(2a^{3}-a^{2}-8a\right){x}^{2}+\left(6a^{3}-7a^{2}-16a+5\right){x}+a^{3}-3a+1$ |
| 31.1-a2 |
31.1-a |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$10.40318$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$363.5855460$ |
2.398663898 |
\( \frac{2166209244918103}{887503681} a^{3} + \frac{1965046325339162}{887503681} a^{2} - \frac{3802966224294038}{887503681} a + \frac{889977164983248}{887503681} \) |
\( \bigl[-a^{3} + a^{2} + 4 a\) , \( a + 1\) , \( a + 1\) , \( 75 a^{3} + 19 a^{2} - 364 a - 252\) , \( -272 a^{3} - 76 a^{2} + 1331 a + 927\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+4a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(75a^{3}+19a^{2}-364a-252\right){x}-272a^{3}-76a^{2}+1331a+927$ |
| 31.1-b1 |
31.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$10.40318$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$220.8018673$ |
0.728342303 |
\( -\frac{19049067382}{29791} a^{3} - \frac{5512270820}{29791} a^{2} + \frac{93644765890}{29791} a + \frac{65326096677}{29791} \) |
\( \bigl[a\) , \( 2 a^{3} - a^{2} - 10 a + 1\) , \( a^{2} - 2\) , \( 3 a^{3} - 3 a^{2} - 16 a + 6\) , \( 2 a^{3} - 2 a^{2} - 10 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(2a^{3}-a^{2}-10a+1\right){x}^{2}+\left(3a^{3}-3a^{2}-16a+6\right){x}+2a^{3}-2a^{2}-10a+2$ |
| 31.1-b2 |
31.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( 31^{6} \) |
$10.40318$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$110.4009336$ |
0.728342303 |
\( \frac{2166209244918103}{887503681} a^{3} + \frac{1965046325339162}{887503681} a^{2} - \frac{3802966224294038}{887503681} a + \frac{889977164983248}{887503681} \) |
\( \bigl[1\) , \( 2 a^{3} - a^{2} - 8 a\) , \( a^{3} - 5 a\) , \( -15 a^{3} + 23 a^{2} + 61 a - 74\) , \( -144 a^{3} + 120 a^{2} + 633 a - 248\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-5a\right){y}={x}^{3}+\left(2a^{3}-a^{2}-8a\right){x}^{2}+\left(-15a^{3}+23a^{2}+61a-74\right){x}-144a^{3}+120a^{2}+633a-248$ |
| 35.1-a1 |
35.1-a |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7 \) |
$10.56220$ |
$(a^3-5a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.062006208$ |
$1864.983882$ |
3.051638159 |
\( -\frac{116224}{175} a^{3} + \frac{615616}{175} a^{2} + \frac{171776}{175} a + \frac{124864}{175} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a\) , \( a + 1\) , \( -a^{3} + 5 a + 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a^{3}+5a+3\right){x}$ |
| 35.1-a2 |
35.1-a |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{2} \) |
$10.56220$ |
$(a^3-5a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.124012416$ |
$932.4919411$ |
3.051638159 |
\( \frac{3651712}{245} a^{3} - \frac{2861248}{245} a^{2} - \frac{16142848}{245} a + \frac{5419648}{245} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( -11 a^{3} + 9 a^{2} + 45 a - 10\) , \( -19 a^{3} + 13 a^{2} + 88 a - 26\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(-a^{3}+a^{2}+4a\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(-11a^{3}+9a^{2}+45a-10\right){x}-19a^{3}+13a^{2}+88a-26$ |
| 35.1-b1 |
35.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5 \cdot 7^{2} \) |
$10.56220$ |
$(a^3-5a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.108401646$ |
$711.9667293$ |
2.036659168 |
\( \frac{3651712}{245} a^{3} - \frac{2861248}{245} a^{2} - \frac{16142848}{245} a + \frac{5419648}{245} \) |
\( \bigl[a^{2} - a - 1\) , \( 2 a^{3} - a^{2} - 9 a\) , \( a^{3} - 5 a - 1\) , \( 2 a^{3} - a^{2} - 10 a + 3\) , \( a^{3} - 6 a\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-5a-1\right){y}={x}^{3}+\left(2a^{3}-a^{2}-9a\right){x}^{2}+\left(2a^{3}-a^{2}-10a+3\right){x}+a^{3}-6a$ |
| 35.1-b2 |
35.1-b |
$2$ |
$2$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7 \) |
$10.56220$ |
$(a^3-5a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.054200823$ |
$1423.933458$ |
2.036659168 |
\( -\frac{116224}{175} a^{3} + \frac{615616}{175} a^{2} + \frac{171776}{175} a + \frac{124864}{175} \) |
\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{3} + 6 a + 1\) , \( a + 1\) , \( -9 a^{3} + 7 a^{2} + 40 a - 9\) , \( 12 a^{3} - 9 a^{2} - 52 a + 17\bigr] \) |
${y}^2+\left(-a^{3}+a^{2}+5a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+6a+1\right){x}^{2}+\left(-9a^{3}+7a^{2}+40a-9\right){x}+12a^{3}-9a^{2}-52a+17$ |
| 37.1-a1 |
37.1-a |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$10.63582$ |
$(-a^3-a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$193.4590824$ |
2.552594963 |
\( \frac{33488364}{37} a^{3} + \frac{80654314}{37} a^{2} + \frac{22816757}{37} a - \frac{14397746}{37} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 6 a + 1\) , \( a^{3} - 4 a\) , \( -8 a^{3} + 5 a^{2} + 35 a - 6\) , \( -11 a^{3} + 7 a^{2} + 48 a - 12\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+6a+1\right){x}^{2}+\left(-8a^{3}+5a^{2}+35a-6\right){x}-11a^{3}+7a^{2}+48a-12$ |
| 37.1-b1 |
37.1-b |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$10.63582$ |
$(-a^3-a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.019091708$ |
$1319.711491$ |
1.329770135 |
\( \frac{33488364}{37} a^{3} + \frac{80654314}{37} a^{2} + \frac{22816757}{37} a - \frac{14397746}{37} \) |
\( \bigl[a^{3} - 5 a\) , \( a^{2} - a - 2\) , \( 1\) , \( -a^{2} + a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-5a\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-a^{2}+a+1\right){x}$ |
| 52.1-a1 |
52.1-a |
$1$ |
$1$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{20} \cdot 13 \) |
$11.09804$ |
$(-a^3+a^2+4a), (a^2+a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$74.59052689$ |
1.968368720 |
\( -\frac{3573599}{52} a^{3} + \frac{21522383}{416} a^{2} + \frac{31698325}{104} a - \frac{37594293}{416} \) |
\( \bigl[1\) , \( a^{3} - 5 a\) , \( 1\) , \( -19 a^{3} + 39 a^{2} + 23 a - 9\) , \( -30 a^{3} + 59 a^{2} + 38 a - 16\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-19a^{3}+39a^{2}+23a-9\right){x}-30a^{3}+59a^{2}+38a-16$ |
| 52.1-b1 |
52.1-b |
$2$ |
$3$ |
4.4.5744.1 |
$4$ |
$[4, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( - 2^{2} \cdot 13^{2} \) |
$11.09804$ |
$(-a^3+a^2+4a), (a^2+a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$810.1340047$ |
2.375402079 |
\( \frac{10537}{169} a^{3} + \frac{127523}{338} a^{2} + \frac{140145}{338} a - \frac{51361}{338} \) |
\( \bigl[a\) , \( a + 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+a^{2}+5a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{3}+a^{2}+5a-1\right){x}$ |
*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.
