| 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 |
| 33124.1-a1 |
33124.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{40} \cdot 7^{6} \cdot 13^{4} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.220089901$ |
3.981576126 |
\( \frac{71903073502287}{60782804992} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 866\) , \( 6445\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+866{x}+6445$ |
| 33124.1-a2 |
33124.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{20} \cdot 7^{12} \cdot 13^{8} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \) |
$1$ |
$0.110044950$ |
3.981576126 |
\( \frac{8511781274893233}{3440817243136} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4254\) , \( 59693\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4254{x}+59693$ |
| 33124.1-a3 |
33124.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 7^{24} \cdot 13^{4} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.055022475$ |
3.981576126 |
\( \frac{3389174547561866673}{74853681183008} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -31294\) , \( -2081875\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31294{x}-2081875$ |
| 33124.1-a4 |
33124.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 7^{6} \cdot 13^{16} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$1$ |
$0.055022475$ |
3.981576126 |
\( \frac{22868021811807457713}{8953460393696} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -59134\) , \( 5547693\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-59134{x}+5547693$ |
| 33124.1-b1 |
33124.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.256426207$ |
1.391677390 |
\( -\frac{424962187484640625}{182} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -15663\) , \( -755809\bigr] \) |
${y}^2+{x}{y}={x}^{3}-15663{x}-755809$ |
| 33124.1-b2 |
33124.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{6} \cdot 7^{6} \cdot 13^{6} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{3} \) |
$1$ |
$0.769278622$ |
1.391677390 |
\( -\frac{795309684625}{6028568} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -193\) , \( -1055\bigr] \) |
${y}^2+{x}{y}={x}^{3}-193{x}-1055$ |
| 33124.1-b3 |
33124.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{18} \cdot 7^{2} \cdot 13^{2} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.307835866$ |
1.391677390 |
\( \frac{37595375}{46592} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 7\) , \( -7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+7{x}-7$ |
| 33124.1-c1 |
33124.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{22} \cdot 7^{14} \cdot 13^{2} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 7 \cdot 11 \) |
$1$ |
$0.175111233$ |
8.130895635 |
\( -\frac{10824513276632329}{21926008832} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -4609\) , \( 120244\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-4609{x}+120244$ |
| 33124.1-d1 |
33124.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 7^{6} \cdot 13^{2} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$3.051746300$ |
5.520816782 |
\( \frac{4019679}{8918} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3\) , \( -5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+3{x}-5$ |
| 33124.1-e1 |
33124.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
33124.1 |
\( 2^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{14} \cdot 7^{2} \cdot 13^{10} \) |
$3.99826$ |
$(2), (7), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 5 \cdot 7 \) |
$1$ |
$0.533192753$ |
11.25345648 |
\( -\frac{1207949625}{332678528} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -22\) , \( 884\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-22{x}+884$ |
*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.
