| 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 |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
1.098969828 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 250250 a - 969716\) , \( -134564648 a + 521170522\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(250250a-969716\right){x}-134564648a+521170522$ |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{10} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
1.098969828 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 330 a - 1276\) , \( -12208 a + 47282\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(330a-1276\right){x}-12208a+47282$ |
| 121.1-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
1.098969828 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 36\) , \( 72 a - 278\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-36\right){x}+72a-278$ |
| 121.1-b1 |
121.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.3 |
$625$ |
\( 1 \) |
$1$ |
$0.064435690$ |
5.199132406 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 250250 a - 969716\) , \( 134564648 a - 521170522\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(250250a-969716\right){x}+134564648a-521170522$ |
| 121.1-b2 |
121.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{10} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$1$ |
\( 5^{2} \) |
$1$ |
$1.610892258$ |
5.199132406 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 330 a - 1276\) , \( 12208 a - 47282\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(330a-1276\right){x}+12208a-47282$ |
| 121.1-b3 |
121.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$40.27230645$ |
5.199132406 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 36\) , \( -72 a + 278\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-36\right){x}-72a+278$ |
| 121.1-c1 |
121.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.064435690$ |
0.207965296 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 121.1-c2 |
121.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$1.610892258$ |
0.207965296 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 121.1-c3 |
121.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$40.27230645$ |
0.207965296 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 121.1-d1 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
1.098969828 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -7820\) , \( 263576\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-7820{x}+263576$ |
| 121.1-d2 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
1.098969828 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -10\) , \( 16\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-10{x}+16$ |
| 121.1-d3 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.29568$ |
$(a+2), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
1.098969828 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( -4\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-4$ |
*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.
