| 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 |
| 64.1-CMa1 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$0.50549$ |
$(a+1)$ |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.875185818$ |
0.429699113 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 64.1-CMa2 |
64.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$0.50549$ |
$(a+1)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{yes}$ |
$-16$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.875185818$ |
0.429699113 |
\( 287496 \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 2\) , \( 3 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+2{x}+3i$ |
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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.
