| 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 |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$6.65434$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$0.740617449$ |
0.144899134 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$6.65434$ |
$(11,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$3.703087246$ |
0.144899134 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$6.65434$ |
$(11,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$18.51543623$ |
0.144899134 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{2} \) |
$6.65434$ |
$(11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$53.24259699$ |
$0.740617449$ |
7.714806207 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -31281\) , \( 2139919\bigr] \) |
${y}^2={x}^3-{x}^2-31281{x}+2139919$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{10} \) |
$6.65434$ |
$(11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$2.129703879$ |
$3.703087246$ |
7.714806207 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 199\bigr] \) |
${y}^2={x}^3-{x}^2-41{x}+199$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{2} \) |
$6.65434$ |
$(11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$2.129703879$ |
$18.51543623$ |
7.714806207 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -1\bigr] \) |
${y}^2={x}^3-{x}^2-{x}-1$ |
| 11.1-c1 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \cdot 19^{12} \) |
$6.65434$ |
$(11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$150.2059778$ |
$0.740617449$ |
21.76471614 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -2823140\) , \( 1824832093\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-2823140{x}+1824832093$ |
| 11.1-c2 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \cdot 19^{12} \) |
$6.65434$ |
$(11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$6.008239113$ |
$3.703087246$ |
21.76471614 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -3730\) , \( 157593\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-3730{x}+157593$ |
| 11.1-c3 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \cdot 19^{12} \) |
$6.65434$ |
$(11,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$6.008239113$ |
$18.51543623$ |
21.76471614 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -120\) , \( -1247\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-120{x}-1247$ |
| 11.1-d1 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$6.65434$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$100$ |
\( 2 \) |
$1$ |
$0.740617449$ |
3.622478355 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -946260\) , \( 354609639\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-946260{x}+354609639$ |
| 11.1-d2 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{22} \) |
$6.65434$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$3.703087246$ |
3.622478355 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-1250{x}+31239$ |
| 11.1-d3 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-418}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$6.65434$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$4$ |
\( 2 \) |
$1$ |
$18.51543623$ |
3.622478355 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -40\) , \( -221\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-40{x}-221$ |
*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.
