| 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 |
$1$ |
$1$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$3.924096890$ |
$3.276723809$ |
2.949869192 |
\( \frac{34283253760}{11} a - \frac{149437227008}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 129 a + 566\) , \( 1092 a + 4761\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(129a+566\right){x}+1092a+4761$ |
| 121.1-b1 |
121.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.364770440$ |
$20.87645860$ |
1.747027197 |
\( -\frac{34283253760}{11} a - \frac{149437227008}{11} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -129 a + 566\) , \( 1092 a - 4766\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-129a+566\right){x}+1092a-4766$ |
| 121.1-c1 |
121.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$5.612837583$ |
$8.512583687$ |
10.96142633 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -7820\) , \( 263575\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-7820{x}+263575$ |
| 121.1-c2 |
121.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 5 \) |
$1.122567516$ |
$8.512583687$ |
10.96142633 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -10\) , \( 15\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-10{x}+15$ |
| 121.1-c3 |
121.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$5.612837583$ |
$8.512583687$ |
10.96142633 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( -5\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-5$ |
| 121.1-d1 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$86.96884564$ |
$0.064435690$ |
1.285622281 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7820{x}-263580$ |
| 121.1-d2 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{10} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$17.39376912$ |
$1.610892258$ |
1.285622281 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$ |
| 121.1-d3 |
121.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$3.478753825$ |
$40.27230645$ |
1.285622281 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}$ |
| 121.1-e1 |
121.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$3.924096890$ |
$3.276723809$ |
2.949869192 |
\( -\frac{34283253760}{11} a - \frac{149437227008}{11} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -129 a + 566\) , \( -1092 a + 4761\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-129a+566\right){x}-1092a+4761$ |
| 121.1-f1 |
121.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.58370$ |
$(11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.364770440$ |
$20.87645860$ |
1.747027197 |
\( \frac{34283253760}{11} a - \frac{149437227008}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 129 a + 566\) , \( -1092 a - 4766\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(129a+566\right){x}-1092a-4766$ |
*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.
