| Curve name |
$X_{256}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 0 \\ 0 & 5 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 2 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{66}$ |
| Curves that $X_{256}$ minimally covers |
$X_{66}$, $X_{67}$, $X_{90}$, $X_{91}$, $X_{128}$, $X_{141}$, $X_{144}$ |
| Curves that minimally cover $X_{256}$ |
$X_{600}$, $X_{601}$ |
| Curves that minimally cover $X_{256}$ and have infinitely many rational
points. |
|
| Model |
A model was not computed. This curve is covered by $X_{53}$, which only has finitely many rational points. |
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
None |
| Generic density of odd order reductions |
N/A |