| Curve name |
$X_{91}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 3 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 2 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 0 & 5 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{39}$ |
| Curves that $X_{91}$ minimally covers |
$X_{39}$, $X_{43}$, $X_{50}$ |
| Curves that minimally cover $X_{91}$ |
$X_{256}$, $X_{259}$, $X_{261}$, $X_{276}$, $X_{286}$, $X_{287}$, $X_{288}$, $X_{289}$, $X_{290}$, $X_{291}$, $X_{300}$, $X_{352}$ |
| Curves that minimally cover $X_{91}$ and have infinitely many rational
points. |
$X_{288}$, $X_{289}$, $X_{291}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{91}) = \mathbb{Q}(f_{91}), f_{39} =
\frac{f_{91}^{2} + 2}{f_{91}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy + y = x^3 - 8786x - 296215$, with conductor $11109$ |
| Generic density of odd order reductions |
$401/1792$ |