| 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 |
| 361.1-a1 |
361.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
361.1 |
\( 19^{2} \) |
\( 19^{2} \) |
$0.77901$ |
$(19)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.935309008$ |
0.935309008 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$ |
| 29241.1-b1 |
29241.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
29241.1 |
\( 3^{4} \cdot 19^{2} \) |
\( 3^{12} \cdot 19^{2} \) |
$2.33704$ |
$(3), (19)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$5.606459454$ |
$0.311769669$ |
3.107420464 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( 0\) , \( i\) , \( -6924\) , \( -221760\bigr] \) |
${y}^2+i{y}={x}^{3}-6924{x}-221760$ |
| 92416.1-b1 |
92416.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
92416.1 |
\( 2^{8} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$3.11606$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1.365713112$ |
$0.467654504$ |
5.109455107 |
\( -\frac{50357871050752}{19} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3077\) , \( -64681\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3077{x}-64681$ |
Download displayed columns to
Pari/GP
SageMath
Magma
Oscar
*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.
