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-a2 |
3872.14-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{14} \cdot 11^{8} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.146127939$ |
$1.228922425$ |
2.171994331 |
\( \frac{59776471}{29282} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 24 a - 8\) , \( -18 a - 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(24a-8\right){x}-18a-26$ |
3872.5-a2 |
3872.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{14} \cdot 11^{8} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.146127939$ |
$1.228922425$ |
2.171994331 |
\( \frac{59776471}{29282} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -24 a + 16\) , \( 18 a - 44\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-24a+16\right){x}+18a-44$ |
5324.6-b2 |
5324.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{2} \cdot 11^{14} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.741068105$ |
2.240779327 |
\( \frac{59776471}{29282} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -64 a + 8\) , \( -136 a + 138\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-64a+8\right){x}-136a+138$ |
5324.7-e2 |
5324.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{2} \cdot 11^{14} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.741068105$ |
2.240779327 |
\( \frac{59776471}{29282} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 66 a - 58\) , \( 71 a + 59\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(66a-58\right){x}+71a+59$ |
15488.20-f3 |
15488.20-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{20} \cdot 11^{8} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.418339135$ |
$0.868979380$ |
6.354298938 |
\( \frac{59776471}{29282} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -40 a + 55\) , \( 6 a - 33\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-40a+55\right){x}+6a-33$ |
15488.5-f3 |
15488.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{20} \cdot 11^{8} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.418339135$ |
$0.868979380$ |
6.354298938 |
\( \frac{59776471}{29282} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 40 a + 16\) , \( 10 a - 124\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a+16\right){x}+10a-124$ |
23716.5-o3 |
23716.5-o |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 7^{6} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.928978033$ |
5.617931086 |
\( \frac{59776471}{29282} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -57\) , \( 41\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-57{x}+41$ |
*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.