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 |
3703.2-a1 |
3703.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3703.2 |
\( 7 \cdot 23^{2} \) |
\( 7 \cdot 23^{10} \) |
$1.84428$ |
$(-2a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.617621489$ |
0.466877961 |
\( -\frac{70052978975990418}{548176896967} a - \frac{50872296108706911}{548176896967} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -90 a + 351\) , \( 1496 a + 394\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-90a+351\right){x}+1496a+394$ |
3703.2-a2 |
3703.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3703.2 |
\( 7 \cdot 23^{2} \) |
\( 7 \cdot 23^{10} \) |
$1.84428$ |
$(-2a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.617621489$ |
0.466877961 |
\( \frac{70052978975990418}{548176896967} a - \frac{120925275084697329}{548176896967} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 90 a + 261\) , \( -1496 a + 1890\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(90a+261\right){x}-1496a+1890$ |
3703.2-a3 |
3703.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3703.2 |
\( 7 \cdot 23^{2} \) |
\( 7^{2} \cdot 23^{8} \) |
$1.84428$ |
$(-2a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.235242978$ |
0.466877961 |
\( \frac{2014698447}{1958887} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 26\) , \( 36\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+26{x}+36$ |
3703.2-a4 |
3703.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3703.2 |
\( 7 \cdot 23^{2} \) |
\( 7^{4} \cdot 23^{4} \) |
$1.84428$ |
$(-2a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.470485956$ |
0.466877961 |
\( \frac{72511713}{25921} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9\) , \( 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-9{x}+8$ |
3703.2-a5 |
3703.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3703.2 |
\( 7 \cdot 23^{2} \) |
\( 7^{2} \cdot 23^{2} \) |
$1.84428$ |
$(-2a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.940971913$ |
0.466877961 |
\( \frac{5545233}{161} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4{x}-2$ |
3703.2-a6 |
3703.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3703.2 |
\( 7 \cdot 23^{2} \) |
\( 7^{8} \cdot 23^{2} \) |
$1.84428$ |
$(-2a+1), (-2a+5), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.235242978$ |
0.466877961 |
\( \frac{209267191953}{55223} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -124\) , \( 560\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-124{x}+560$ |
*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.