| 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-d6 |
3872.14-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.239173832$ |
2.892774765 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2738 a - 4105\) , \( -87547 a + 61119\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2738a-4105\right){x}-87547a+61119$ |
| 3872.5-d6 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.239173832$ |
2.892774765 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2140 a + 4619\) , \( -46032 a - 77943\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2140a+4619\right){x}-46032a-77943$ |
| 5324.6-d6 |
5324.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{15} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.982477394$ |
$0.144227247$ |
3.427684460 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -8298 a + 10087\) , \( -17537 a + 545409\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-8298a+10087\right){x}-17537a+545409$ |
| 5324.7-c6 |
5324.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{15} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.964954788$ |
$0.144227247$ |
3.427684460 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 4707 a - 13169\) , \( 291111 a - 525613\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4707a-13169\right){x}+291111a-525613$ |
| 15488.20-c5 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.169121438$ |
1.022750326 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1372 a + 9579\) , \( -237584 a + 17845\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1372a+9579\right){x}-237584a+17845$ |
| 15488.5-c5 |
15488.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.169121438$ |
1.022750326 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6757 a - 4956\) , \( -216039 a - 63823\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6757a-4956\right){x}-216039a-63823$ |
| 23716.5-e5 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.180798422$ |
1.093366089 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4188 a - 3596\) , \( 192280 a + 13020\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4188a-3596\right){x}+192280a+13020$ |
*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.
