| 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-d3 |
3872.14-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{36} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 138 a + 159\) , \( 623 a - 1831\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(138a+159\right){x}+623a-1831$ |
| 3872.5-d3 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{36} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -178 a - 86\) , \( 1188 a - 129\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-178a-86\right){x}+1188a-129$ |
| 5324.6-d3 |
5324.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{24} \cdot 11^{12} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.982477394$ |
$0.288454494$ |
3.427684460 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -307 a - 542\) , \( -4407 a - 3414\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-307a-542\right){x}-4407a-3414$ |
| 5324.7-c3 |
5324.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{24} \cdot 11^{12} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.491238697$ |
$0.288454494$ |
3.427684460 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 537 a + 109\) , \( 192 a + 7744\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(537a+109\right){x}+192a+7744$ |
| 15488.20-c4 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{42} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -437 a + 119\) , \( 3199 a - 3493\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-437a+119\right){x}+3199a-3493$ |
| 15488.5-c4 |
15488.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{42} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 92 a + 527\) , \( 3344 a - 3163\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(92a+527\right){x}+3344a-3163$ |
| 23716.5-e4 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{6} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.361596845$ |
1.093366089 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 269 a - 504\) , \( -2732 a + 2524\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(269a-504\right){x}-2732a+2524$ |
*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.
