| 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 |
| 3872.14-a4 |
3872.14-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.584511757$ |
$2.457844850$ |
2.171994331 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a + 22\) , \( 26 a - 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+22\right){x}+26a-14$ |
| 3872.5-a4 |
3872.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{17} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.584511757$ |
$2.457844850$ |
2.171994331 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -3 a - 19\) , \( -a + 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-19\right){x}-a+31$ |
| 5324.6-b4 |
5324.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{5} \cdot 11^{8} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.482136211$ |
2.240779327 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 9 a - 62\) , \( 51 a - 162\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-62\right){x}+51a-162$ |
| 5324.7-e4 |
5324.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{5} \cdot 11^{8} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.482136211$ |
2.240779327 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 16 a + 46\) , \( -130 a + 160\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(16a+46\right){x}-130a+160$ |
| 15488.20-f1 |
15488.20-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.418339135$ |
$1.737958760$ |
6.354298938 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -22 a - 22\) , \( 67 a + 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-22\right){x}+67a+11$ |
| 15488.5-f1 |
15488.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{23} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.418339135$ |
$1.737958760$ |
6.354298938 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -16 a + 45\) , \( 73 a + 50\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-16a+45\right){x}+73a+50$ |
| 23716.5-o1 |
23716.5-o |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{6} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.857956067$ |
5.617931086 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 28 a - 18\) , \( -47 a - 46\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(28a-18\right){x}-47a-46$ |
*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.
