| 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 |
| 12482.1-a1 |
12482.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$1.88903$ |
$(a+1), (79)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.065679403$ |
$4.669865363$ |
2.453711786 |
\( \frac{4826809}{316} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -3\) , \( -1\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-3{x}-1$ |
| 12482.1-b1 |
12482.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{12} \cdot 79^{6} \) |
$1.88903$ |
$(a+1), (79)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$0.770200930$ |
2.053869146 |
\( \frac{59914169497}{31554496} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -81\) , \( 92\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-81{x}+92$ |
| 12482.1-b2 |
12482.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$1.88903$ |
$(a+1), (79)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$2.310602790$ |
2.053869146 |
\( \frac{11134383337}{316} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -46\) , \( -118\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-46{x}-118$ |
| 12482.1-b3 |
12482.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{36} \cdot 79^{2} \) |
$1.88903$ |
$(a+1), (79)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$0.256733643$ |
2.053869146 |
\( \frac{15698803397448457}{20709376} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -5216\) , \( 145452\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-5216{x}+145452$ |
| 12482.1-c1 |
12482.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{16} \cdot 79^{2} \) |
$1.88903$ |
$(a+1), (79)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.038990280$ |
$2.542517964$ |
3.172271620 |
\( \frac{72511713}{20224} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -8\) , \( -9\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-8{x}-9$ |
| 12482.1-d1 |
12482.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{4} \cdot 79^{2} \) |
$1.88903$ |
$(a+1), (79)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.325599747$ |
$5.333879182$ |
3.473419430 |
\( \frac{103823}{316} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 2\) , \( -1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+2{x}-1$ |
| 12482.1-d2 |
12482.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{2} \cdot 79^{4} \) |
$1.88903$ |
$(a+1), (79)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.651199495$ |
$2.666939591$ |
3.473419430 |
\( \frac{81182737}{12482} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -8\) , \( -5\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-8{x}-5$ |
| 12482.1-e1 |
12482.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{40} \cdot 79^{2} \) |
$1.88903$ |
$(a+1), (79)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$2.761268255$ |
$0.509267787$ |
4.499919920 |
\( \frac{8194759433281}{82837504} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -419\) , \( -3109\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-419{x}-3109$ |
| 12482.1-e2 |
12482.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12482.1 |
\( 2 \cdot 79^{2} \) |
\( 2^{8} \cdot 79^{10} \) |
$1.88903$ |
$(a+1), (79)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.552253651$ |
$0.101853557$ |
4.499919920 |
\( \frac{1413378216646643521}{49232902384} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -23380\) , \( -1385691\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-23380{x}-1385691$ |
*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.
