| Curve name |
$X_{533}$ |
| Index |
$96$ |
| Level |
$32$ |
| Genus |
$2$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 3 \\ 2 & 19 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 10 & 31 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 10 & 31 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{216}$ |
| Curves that $X_{533}$ minimally covers |
$X_{216}$ |
| Curves that minimally cover $X_{533}$ |
|
| Curves that minimally cover $X_{533}$ and have infinitely many rational
points. |
|
| Model |
\[y^2 = -x^6 + 8x^5 - 6x^4 - 12x^2 - 32x - 8\] |
| Info about rational points |
No non-singular rational points |
| Comments on finding rational points |
The rank of the Jacobian is 0. We use the method of Chabauty. |
| Elliptic curve whose $2$-adic image is the subgroup |
None |
| Generic density of odd order reductions |
N/A |