| 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 |
| 121.2-a1 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.78412$ |
$(-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$0.555680735$ |
$0.370308724$ |
0.311100175 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 7744.2-d1 |
7744.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.2 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{6} \cdot 11^{2} \) |
$2.21783$ |
$(a), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.261847810$ |
4.948458482 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -7820 a + 15640\) , \( -263580 a - 527159\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-7820a+15640\right){x}-263580a-527159$ |
| 7744.20-d1 |
7744.20-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.20 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{6} \cdot 11^{2} \) |
$2.21783$ |
$(-a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.261847810$ |
4.948458482 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 7820 a + 7820\) , \( 263579 a - 790739\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7820a+7820\right){x}+263579a-790739$ |
| 9801.2-d1 |
9801.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9801.2 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{2} \) |
$2.35237$ |
$(-2a+3), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$66.01014894$ |
$0.123436241$ |
12.31868567 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -70383\) , \( 7187035\bigr] \) |
${y}^2+{y}={x}^{3}-70383{x}+7187035$ |
| 14641.3-d1 |
14641.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14641.3 |
\( 11^{4} \) |
\( 11^{14} \) |
$2.60064$ |
$(-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$70.51588395$ |
$0.033664429$ |
14.35585873 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -946260\) , \( 354609639\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-946260{x}+354609639$ |
| 21296.18-b1 |
21296.18-b |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.18 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{8} \) |
$2.85603$ |
$(-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$15.66283288$ |
$0.055826140$ |
2.643923513 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 101664 a - 367556\) , \( 33150792 a - 80599764\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(101664a-367556\right){x}+33150792a-80599764$ |
| 21296.19-d1 |
21296.19-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.19 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{8} \) |
$2.85603$ |
$(-a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.055826140$ |
4.220059573 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 39102 a + 320633\) , \( -57350008 a + 46076331\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(39102a+320633\right){x}-57350008a+46076331$ |
| 21296.2-d1 |
21296.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.2 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{8} \) |
$2.85603$ |
$(a), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.055826140$ |
4.220059573 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -39102 a + 359735\) , \( 57350007 a - 11273676\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-39102a+359735\right){x}+57350007a-11273676$ |
| 21296.3-b1 |
21296.3-b |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.3 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{8} \) |
$2.85603$ |
$(a), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$15.66283288$ |
$0.055826140$ |
2.643923513 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -101664 a - 265892\) , \( -33150793 a - 47448971\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-101664a-265892\right){x}-33150793a-47448971$ |
| 30976.14-b1 |
30976.14-b |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.14 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$3.13649$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$30.46889473$ |
$0.092577181$ |
4.264534427 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -125125\) , \( 16994227\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-125125{x}+16994227$ |
*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.
