| Curve name |
$X_{257}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 4 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 7 & 3 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 4 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 2 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{64}$ |
| Curves that $X_{257}$ minimally covers |
$X_{64}$, $X_{70}$, $X_{76}$, $X_{77}$, $X_{133}$, $X_{136}$, $X_{137}$ |
| Curves that minimally cover $X_{257}$ |
$X_{443}$, $X_{599}$ |
| Curves that minimally cover $X_{257}$ 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 |