| Curve name |
$X_{128}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 2 \\ 2 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 6 & 3 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 0 & 5 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{28}$ |
| Curves that $X_{128}$ minimally covers |
$X_{28}$, $X_{39}$, $X_{53}$ |
| Curves that minimally cover $X_{128}$ |
$X_{256}$, $X_{264}$, $X_{372}$, $X_{390}$ |
| Curves that minimally cover $X_{128}$ 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 |