| 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-a1 |
392.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0.79523$ |
$(a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.059979974$ |
$6.395739286$ |
0.767232560 |
\( -\frac{4}{7} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}-i{x}$ |
| 12544.1-f1 |
12544.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12544.1 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.89137$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.197869643$ |
3.197869643 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 0\) , \( -4 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}-4i$ |
| 19208.1-f1 |
19208.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{8} \cdot 7^{14} \) |
$2.10397$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.913677040$ |
3.654708163 |
\( -\frac{4}{7} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 4\) , \( -174 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+4{x}-174i$ |
| 19600.1-c1 |
19600.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 7^{2} \) |
$2.11462$ |
$(a+1), (-a-2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.860261562$ |
2.860261562 |
\( -\frac{4}{7} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -i\) , \( 5 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}-i{x}+5i+1$ |
| 19600.3-c1 |
19600.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
19600.3 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 7^{2} \) |
$2.11462$ |
$(a+1), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.860261562$ |
2.860261562 |
\( -\frac{4}{7} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -i\) , \( -6 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}-i{x}-6i+1$ |
| 31752.1-j1 |
31752.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
31752.1 |
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 7^{2} \) |
$2.38568$ |
$(a+1), (3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.131913095$ |
4.263826191 |
\( -\frac{4}{7} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 0\) , \( 14 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+14i$ |
| 50176.1-b1 |
50176.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{2} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.261235310$ |
2.261235310 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 0\) , \( -8 i + 8\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}-8i+8$ |
| 50176.1-q1 |
50176.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
50176.1 |
\( 2^{10} \cdot 7^{2} \) |
\( 2^{26} \cdot 7^{2} \) |
$2.67481$ |
$(a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.261235310$ |
2.261235310 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 0\) , \( 8 i + 8\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+8i+8$ |
*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.
