| 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 |
| 15876.3-a1 |
15876.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{4} \) |
$2.83706$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.097774690$ |
$1.274441630$ |
4.229340360 |
\( -\frac{16384}{147} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( 65\bigr] \) |
${y}^2={x}^{3}-12{x}+65$ |
| 15876.3-a2 |
15876.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{2} \) |
$2.83706$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.195549380$ |
$1.274441630$ |
4.229340360 |
\( \frac{20720464}{63} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -81\) , \( -243\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-81{x}-243$ |
| 15876.3-b1 |
15876.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 7^{12} \) |
$2.83706$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$6.150609675$ |
$0.290810614$ |
5.059101756 |
\( -\frac{10061824000}{352947} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1020\) , \( 12913\bigr] \) |
${y}^2={x}^{3}-1020{x}+12913$ |
| 15876.3-b2 |
15876.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 7^{4} \) |
$2.83706$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.050203225$ |
$0.872431843$ |
5.059101756 |
\( \frac{2048000}{1323} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 60\) , \( 61\bigr] \) |
${y}^2={x}^{3}+60{x}+61$ |
| 15876.3-b3 |
15876.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{24} \cdot 7^{2} \) |
$2.83706$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1.025101612$ |
$0.872431843$ |
5.059101756 |
\( \frac{9826000}{5103} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -63\) , \( -31\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-63{x}-31$ |
| 15876.3-b4 |
15876.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
15876.3 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{6} \) |
$2.83706$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$3.075304837$ |
$0.290810614$ |
5.059101756 |
\( \frac{2640279346000}{3087} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -4113\) , \( -99499\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4113{x}-99499$ |
*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.
