| 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 |
| 24964.1-a1 |
24964.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{16} \cdot 79^{2} \) |
$3.72532$ |
$(2), (79)$ |
$3$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.039162963$ |
$2.542517964$ |
3.842847999 |
\( \frac{72511713}{20224} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-9{x}+9$ |
| 24964.1-b1 |
24964.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$4$ |
\( 2 \) |
$0.079168762$ |
$4.669865363$ |
3.567071822 |
\( \frac{4826809}{316} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 24964.1-c1 |
24964.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{40} \cdot 79^{2} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 2^{2} \cdot 5 \) |
$2.008203969$ |
$0.509267787$ |
3.947004804 |
\( \frac{8194759433281}{82837504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -420\) , \( 3109\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-420{x}+3109$ |
| 24964.1-c2 |
24964.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{8} \cdot 79^{10} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$4$ |
\( 2^{2} \cdot 5 \) |
$0.401640793$ |
$0.101853557$ |
3.947004804 |
\( \frac{1413378216646643521}{49232902384} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -23380\) , \( -1385691\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-23380{x}-1385691$ |
| 24964.1-d1 |
24964.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{12} \cdot 79^{6} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1.610193829$ |
$0.770200930$ |
11.96563724 |
\( \frac{59914169497}{31554496} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -82\) , \( -92\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-82{x}-92$ |
| 24964.1-d2 |
24964.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \) |
$4.830581487$ |
$2.310602790$ |
11.96563724 |
\( \frac{11134383337}{316} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -47\) , \( 118\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-47{x}+118$ |
| 24964.1-d3 |
24964.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{36} \cdot 79^{2} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \cdot 3^{2} \) |
$0.536731276$ |
$0.256733643$ |
11.96563724 |
\( \frac{15698803397448457}{20709376} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5217\) , \( -145452\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5217{x}-145452$ |
| 24964.1-e1 |
24964.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.634999215$ |
$5.333879182$ |
8.475343669 |
\( \frac{103823}{316} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+{x}+1$ |
| 24964.1-e2 |
24964.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
24964.1 |
\( 2^{2} \cdot 79^{2} \) |
\( 2^{2} \cdot 79^{4} \) |
$3.72532$ |
$(2), (79)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.269998430$ |
$2.666939591$ |
8.475343669 |
\( \frac{81182737}{12482} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -9\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-9{x}+5$ |
*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.
