| 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 |
$3$ |
$25$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.87441$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$55.63237165$ |
$0.064435690$ |
1.133584921 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 121.1-a2 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$1.87441$ |
$(11)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$11.12647433$ |
$1.610892258$ |
1.133584921 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 121.1-a3 |
121.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.87441$ |
$(11)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$2.225294866$ |
$40.27230645$ |
1.133584921 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 121.1-b1 |
121.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{4} \) |
$1.87441$ |
$(11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.122517629$ |
$25.94968460$ |
1.005380992 |
\( -\frac{21952}{121} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 14 a - 44\) , \( -160 a + 506\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(14a-44\right){x}-160a+506$ |
| 121.1-b2 |
121.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.87441$ |
$(11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.122517629$ |
$51.89936920$ |
1.005380992 |
\( \frac{5088448}{11} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 21 a - 71\) , \( -79 a + 246\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(21a-71\right){x}-79a+246$ |
| 121.1-c1 |
121.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$1.87441$ |
$(11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$25.94968460$ |
8.206010790 |
\( -\frac{21952}{121} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 3 a - 12\) , \( -17 a + 51\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3a-12\right){x}-17a+51$ |
| 121.1-c2 |
121.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$1.87441$ |
$(11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$51.89936920$ |
8.206010790 |
\( \frac{5088448}{11} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 86 a - 272\) , \( -800 a + 2530\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(86a-272\right){x}-800a+2530$ |
| 121.1-d1 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$1.87441$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.3 |
$25$ |
\( 1 \) |
$12.68007523$ |
$0.064435690$ |
6.459342672 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -31281\) , \( -2139919\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-31281{x}-2139919$ |
| 121.1-d2 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{10} \) |
$1.87441$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$1$ |
\( 5 \) |
$2.536015047$ |
$1.610892258$ |
6.459342672 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -199\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-199$ |
| 121.1-d3 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 2^{12} \cdot 11^{2} \) |
$1.87441$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$0.507203009$ |
$40.27230645$ |
6.459342672 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}+1$ |
*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.
