| Curve name |
$X_{251}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 0 \\ 6 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 4 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 4 \\ 0 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{58}$ |
| Curves that $X_{251}$ minimally covers |
$X_{58}$, $X_{61}$, $X_{65}$, $X_{69}$, $X_{136}$, $X_{141}$, $X_{148}$ |
| Curves that minimally cover $X_{251}$ |
$X_{454}$, $X_{536}$, $X_{540}$, $X_{602}$, $X_{670}$ |
| Curves that minimally cover $X_{251}$ 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 |