| 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 |
| 392.1-b4 |
392.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$0.79523$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.008147859$ |
1.004073929 |
\( \frac{1443468546}{7} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 74\) , \( -212 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+74\right){x}-212i$ |
| 12544.1-a4 |
12544.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.979556781$ |
$1.004073929$ |
2.991695286 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 299\) , \( 1990 i\bigr] \) |
${y}^2={x}^{3}+299{x}+1990i$ |
| 19208.1-a4 |
19208.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{10} \cdot 7^{14} \) |
$2.10397$ |
$(a+1), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$7.567836011$ |
$0.286878265$ |
2.171047669 |
\( \frac{1443468546}{7} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 3662\) , \( 87152 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+3662\right){x}+87152i$ |
| 19600.1-a4 |
19600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 5^{6} \cdot 7^{2} \) |
$2.11462$ |
$(a+1), (-a-2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.898071024$ |
1.796142048 |
\( \frac{1443468546}{7} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -300 i - 225\) , \( -2849 i - 348\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-300i-225\right){x}-2849i-348$ |
| 19600.3-a4 |
19600.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.3 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 5^{6} \cdot 7^{2} \) |
$2.11462$ |
$(a+1), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.898071024$ |
1.796142048 |
\( \frac{1443468546}{7} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 298 i - 225\) , \( -2849 i + 348\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(298i-225\right){x}-2849i+348$ |
| 31752.1-e4 |
31752.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
31752.1 |
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.137828769$ |
$0.669382619$ |
3.046571210 |
\( \frac{1443468546}{7} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 672\) , \( 7052 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+672\right){x}+7052i$ |
| 50176.1-e4 |
50176.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{2} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.709987484$ |
2.839949937 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 598 i\) , \( -3980 i - 3980\bigr] \) |
${y}^2={x}^{3}+598i{x}-3980i-3980$ |
| 50176.1-n4 |
50176.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{28} \cdot 7^{2} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.709987484$ |
2.839949937 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -598 i\) , \( 3980 i - 3980\bigr] \) |
${y}^2={x}^{3}-598i{x}+3980i-3980$ |
*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.
