| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.85809$ |
$(a+3), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.700920647$ |
$36.82322769$ |
5.156585325 |
\( \frac{19683}{11} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 7 a + 32\) , \( 7 a + 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a+32\right){x}+7a+30$ |
| 121.1-a2 |
121.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$2.85809$ |
$(a+3), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.350460323$ |
$18.41161384$ |
5.156585325 |
\( \frac{19034163}{121} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -8 a - 33\) , \( 7 a + 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-33\right){x}+7a+30$ |
| 121.1-b1 |
121.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.85809$ |
$(a+3), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.064435690$ |
0.167041745 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 121.1-b2 |
121.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.85809$ |
$(a+3), (a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$1.610892258$ |
0.167041745 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 121.1-b3 |
121.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.85809$ |
$(a+3), (a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$40.27230645$ |
0.167041745 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 121.1-c1 |
121.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.85809$ |
$(a+3), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.700920647$ |
$36.82322769$ |
5.156585325 |
\( \frac{19683}{11} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 7 a + 14\) , \( 8 a + 28\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(7a+14\right){x}+8a+28$ |
| 121.1-c2 |
121.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$2.85809$ |
$(a+3), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.350460323$ |
$18.41161384$ |
5.156585325 |
\( \frac{19034163}{121} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 22 a - 66\) , \( -72 a + 453\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(22a-66\right){x}-72a+453$ |
| 121.1-d1 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.85809$ |
$(a+3), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
0.882713808 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 680369 a - 3620814\) , \( -670563167 a + 3568620089\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(680369a-3620814\right){x}-670563167a+3568620089$ |
| 121.1-d2 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.85809$ |
$(a+3), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
0.882713808 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 899 a - 4784\) , \( -58057 a + 308969\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(899a-4784\right){x}-58057a+308969$ |
| 121.1-d3 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.85809$ |
$(a+3), (a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$8.512583687$ |
0.882713808 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 29 a - 154\) , \( 453 a - 2411\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(29a-154\right){x}+453a-2411$ |
*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.
