| 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-a2 |
121.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
121.2 |
\( 11^{2} \) |
\( 11^{10} \) |
$0.78412$ |
$(-2a+3), (2a+1)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5^{2} \) |
$0.111136147$ |
$1.851543623$ |
0.311100175 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 7744.2-d2 |
7744.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.2 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{6} \cdot 11^{10} \) |
$2.21783$ |
$(a), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 5 \) |
$1$ |
$1.309239051$ |
4.948458482 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -10 a + 20\) , \( -20 a - 39\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-10a+20\right){x}-20a-39$ |
| 7744.20-d2 |
7744.20-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.20 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{6} \cdot 11^{10} \) |
$2.21783$ |
$(-a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 5 \) |
$1$ |
$1.309239051$ |
4.948458482 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 10 a + 10\) , \( 19 a - 59\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a+10\right){x}+19a-59$ |
| 9801.2-d2 |
9801.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9801.2 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{10} \) |
$2.35237$ |
$(-2a+3), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$13.20202978$ |
$0.617181207$ |
12.31868567 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -93\) , \( 625\bigr] \) |
${y}^2+{y}={x}^{3}-93{x}+625$ |
| 14641.3-d2 |
14641.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14641.3 |
\( 11^{4} \) |
\( 11^{22} \) |
$2.60064$ |
$(-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$14.10317679$ |
$0.168322147$ |
14.35585873 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-1250{x}+31239$ |
| 21296.18-b2 |
21296.18-b |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.18 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{16} \) |
$2.85603$ |
$(-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$3.132566576$ |
$0.279130703$ |
2.643923513 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 134 a - 486\) , \( 2732 a - 6944\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(134a-486\right){x}+2732a-6944$ |
| 21296.19-d2 |
21296.19-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.19 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{16} \) |
$2.85603$ |
$(-a+1), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.279130703$ |
4.220059573 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 52 a + 423\) , \( -5138 a + 4041\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(52a+423\right){x}-5138a+4041$ |
| 21296.2-d2 |
21296.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.2 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{16} \) |
$2.85603$ |
$(a), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.279130703$ |
4.220059573 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( -52 a + 475\) , \( 5137 a - 1096\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-52a+475\right){x}+5137a-1096$ |
| 21296.3-b2 |
21296.3-b |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
21296.3 |
\( 2^{4} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{16} \) |
$2.85603$ |
$(a), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$3.132566576$ |
$0.279130703$ |
2.643923513 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -134 a - 352\) , \( -2733 a - 4211\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-134a-352\right){x}-2733a-4211$ |
| 30976.14-b2 |
30976.14-b |
$3$ |
$25$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.14 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{10} \) |
$3.13649$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$6.093778947$ |
$0.462885905$ |
4.264534427 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -165\) , \( 1427\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-165{x}+1427$ |
*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.
