| Curve name |
$X_{195}$ |
| 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 & 6 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{84}$ |
| Curves that $X_{195}$ minimally covers |
$X_{84}$, $X_{92}$, $X_{102}$ |
| Curves that minimally cover $X_{195}$ |
$X_{445}$, $X_{453}$, $X_{479}$, $X_{487}$, $X_{195a}$, $X_{195b}$, $X_{195c}$, $X_{195d}$, $X_{195e}$, $X_{195f}$, $X_{195g}$, $X_{195h}$, $X_{195i}$, $X_{195j}$, $X_{195k}$, $X_{195l}$ |
| Curves that minimally cover $X_{195}$ and have infinitely many rational
points. |
$X_{195a}$, $X_{195b}$, $X_{195c}$, $X_{195d}$, $X_{195e}$, $X_{195f}$, $X_{195g}$, $X_{195h}$, $X_{195i}$, $X_{195j}$, $X_{195k}$, $X_{195l}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{195}) = \mathbb{Q}(f_{195}), f_{84} =
\frac{f_{195}^{2} - \frac{1}{2}}{f_{195}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 + 1714x + 14685$, with conductor $735$ |
| Generic density of odd order reductions |
$25/224$ |