| 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 |
| 1083.2-b2 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.816172249$ |
0.942434535 |
\( \frac{7240152655469734}{50950689123} a - \frac{5512832666599067}{50950689123} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a + 193\) , \( 464 a + 535\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-130a+193\right){x}+464a+535$ |
| 61731.2-b1 |
61731.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.2 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{7} \cdot 19^{16} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.108104655$ |
0.998628029 |
\( \frac{7240152655469734}{50950689123} a - \frac{5512832666599067}{50950689123} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 11237 a - 5950\) , \( 322105 a + 82626\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(11237a-5950\right){x}+322105a+82626$ |
| 61731.3-b1 |
61731.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{7} \cdot 19^{16} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.108104655$ |
0.998628029 |
\( \frac{7240152655469734}{50950689123} a - \frac{5512832666599067}{50950689123} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -9143 a + 10240\) , \( 68164 a + 329450\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9143a+10240\right){x}+68164a+329450$ |
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*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.
