| Curve name |
$X_{202}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{78}$ |
| Curves that $X_{202}$ minimally covers |
$X_{78}$, $X_{85}$, $X_{102}$ |
| Curves that minimally cover $X_{202}$ |
$X_{471}$, $X_{472}$, $X_{473}$, $X_{474}$, $X_{202a}$, $X_{202b}$, $X_{202c}$, $X_{202d}$, $X_{202e}$, $X_{202f}$, $X_{202g}$, $X_{202h}$ |
| Curves that minimally cover $X_{202}$ and have infinitely many rational
points. |
$X_{202a}$, $X_{202b}$, $X_{202c}$, $X_{202d}$, $X_{202e}$, $X_{202f}$, $X_{202g}$, $X_{202h}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{202}) = \mathbb{Q}(f_{202}), f_{78} =
\frac{f_{202}^{2} - \frac{1}{2}}{f_{202}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 8226x + 286474$, with conductor $126$ |
| Generic density of odd order reductions |
$193/1792$ |