| 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 |
| 121.1-a1 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$0.51333$ |
$(11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.370308724$ |
0.427595683 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 14641.1-b1 |
14641.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14641.1 |
\( 11^{4} \) |
\( 11^{14} \) |
$1.70252$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$7.655751664$ |
$0.033664429$ |
2.380775540 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -946260 a + 946260\) , \( 354609639\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-946260a+946260\right){x}+354609639$ |
| 20449.1-a1 |
20449.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20449.1 |
\( 11^{2} \cdot 13^{2} \) |
\( 11^{2} \cdot 13^{6} \) |
$1.85083$ |
$(-4a+1), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$6.923571309$ |
$0.102705161$ |
3.284367889 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -62563 a + 117305\) , \( -9543612 a - 4543418\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-62563a+117305\right){x}-9543612a-4543418$ |
| 20449.3-a1 |
20449.3-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20449.3 |
\( 11^{2} \cdot 13^{2} \) |
\( 11^{2} \cdot 13^{6} \) |
$1.85083$ |
$(4a-3), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$6.923571309$ |
$0.102705161$ |
3.284367889 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 62563 a + 54742\) , \( 9543612 a - 14087030\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(62563a+54742\right){x}+9543612a-14087030$ |
| 30976.1-h1 |
30976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
30976.1 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{2} \) |
$2.05331$ |
$(2), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.092577181$ |
2.672473023 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -125125\) , \( 16994227\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-125125{x}+16994227$ |
| 53361.1-c1 |
53361.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53361.1 |
\( 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{2} \) |
$2.35237$ |
$(-2a+1), (-3a+1), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$10.54640577$ |
$0.080807988$ |
3.936299486 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 117306 a + 70383\) , \( -16072854 a + 29562341\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(117306a+70383\right){x}-16072854a+29562341$ |
| 53361.3-c1 |
53361.3-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
53361.3 |
\( 3^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{2} \) |
$2.35237$ |
$(-2a+1), (3a-2), (11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$10.54640577$ |
$0.080807988$ |
3.936299486 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 187689 a - 70383\) , \( 16072854 a + 13489487\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(187689a-70383\right){x}+16072854a+13489487$ |
| 75625.1-b1 |
75625.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
75625.1 |
\( 5^{4} \cdot 11^{2} \) |
\( 5^{12} \cdot 11^{2} \) |
$2.56664$ |
$(5), (11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.3 |
$25$ |
\( 1 \) |
$1$ |
$0.074061744$ |
2.137978418 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 195508 a\) , \( -33338481\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+195508a{x}-33338481$ |
*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.
