| 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-d4 |
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 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 178 a - 265\) , \( -1275 a + 703\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(178a-265\right){x}-1275a+703$ |
| 3872.5-d4 |
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 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -140 a + 299\) , \( -624 a - 1207\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-140a+299\right){x}-624a-1207$ |
| 5324.6-d4 |
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 |
$1$ |
\( 2^{8} \) |
$0.491238697$ |
$0.288454494$ |
3.427684460 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -538 a + 647\) , \( -193 a + 7937\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-538a+647\right){x}-193a+7937$ |
| 5324.7-c4 |
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 |
$1$ |
\( 2^{7} \) |
$0.982477394$ |
$0.288454494$ |
3.427684460 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 307 a - 849\) , \( 4407 a - 7821\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(307a-849\right){x}+4407a-7821$ |
| 15488.20-c3 |
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 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -92 a + 619\) , \( -3344 a + 181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-92a+619\right){x}-3344a+181$ |
| 15488.5-c3 |
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 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 437 a - 316\) , \( -3079 a - 1167\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(437a-316\right){x}-3079a-1167$ |
| 23716.5-e3 |
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 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -268 a - 236\) , \( 3000 a + 28\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-268a-236\right){x}+3000a+28$ |
*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.
