| Curve name |
$X_{102}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{36}$ |
| Curves that $X_{102}$ minimally covers |
$X_{36}$ |
| Curves that minimally cover $X_{102}$ |
$X_{193}$, $X_{195}$, $X_{197}$, $X_{202}$, $X_{213}$, $X_{223}$, $X_{230}$, $X_{235}$, $X_{338}$, $X_{340}$, $X_{342}$, $X_{347}$, $X_{102a}$, $X_{102b}$, $X_{102c}$, $X_{102d}$, $X_{102e}$, $X_{102f}$, $X_{102g}$, $X_{102h}$, $X_{102i}$, $X_{102j}$, $X_{102k}$, $X_{102l}$, $X_{102m}$, $X_{102n}$, $X_{102o}$, $X_{102p}$ |
| Curves that minimally cover $X_{102}$ and have infinitely many rational
points. |
$X_{193}$, $X_{195}$, $X_{197}$, $X_{202}$, $X_{213}$, $X_{223}$, $X_{230}$, $X_{235}$, $X_{102a}$, $X_{102b}$, $X_{102c}$, $X_{102d}$, $X_{102e}$, $X_{102f}$, $X_{102g}$, $X_{102h}$, $X_{102i}$, $X_{102j}$, $X_{102k}$, $X_{102l}$, $X_{102m}$, $X_{102n}$, $X_{102o}$, $X_{102p}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{102}) = \mathbb{Q}(f_{102}), f_{36} =
\frac{f_{102}^{2}}{f_{102} - 1}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 + x^2 - 975x + 11250$, with conductor $525$ |
| Generic density of odd order reductions |
$19/168$ |