| Curve name |
$X_{90}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 3 \\ 6 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 4 & 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 $X_{90}$ minimally covers |
$X_{28}$, $X_{39}$, $X_{50}$ |
| Curves that minimally cover $X_{90}$ |
$X_{256}$, $X_{262}$, $X_{280}$, $X_{281}$, $X_{282}$, $X_{283}$, $X_{284}$, $X_{285}$ |
| Curves that minimally cover $X_{90}$ and have infinitely many rational
points. |
$X_{281}$, $X_{284}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{90}) = \mathbb{Q}(f_{90}), f_{28} =
\frac{2f_{90}^{2} - 4}{f_{90}^{2} + 4f_{90} + 2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 3371423x + 801711878$, with conductor $16940$ |
| Generic density of odd order reductions |
$1427/5376$ |