| Curve name |
$X_{95}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 4 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 1 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{27}$ |
| Curves that $X_{95}$ minimally covers |
$X_{27}$, $X_{39}$, $X_{49}$ |
| Curves that minimally cover $X_{95}$ |
$X_{221}$, $X_{222}$, $X_{259}$, $X_{260}$, $X_{379}$, $X_{381}$, $X_{95a}$, $X_{95b}$, $X_{95c}$, $X_{95d}$, $X_{95e}$, $X_{95f}$, $X_{95g}$, $X_{95h}$ |
| Curves that minimally cover $X_{95}$ and have infinitely many rational
points. |
$X_{221}$, $X_{222}$, $X_{95a}$, $X_{95b}$, $X_{95c}$, $X_{95d}$, $X_{95e}$, $X_{95f}$, $X_{95g}$, $X_{95h}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{95}) = \mathbb{Q}(f_{95}), f_{27} =
\frac{2}{f_{95}^{2}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy + y = x^3 + 5899x + 478973$, with conductor $7275$ |
| Generic density of odd order reductions |
$289/1792$ |