| Curve name |
$X_{79}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 0 \\ 0 & 5 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 4 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{32}$ |
| Curves that $X_{79}$ minimally covers |
$X_{32}$, $X_{34}$, $X_{44}$ |
| Curves that minimally cover $X_{79}$ |
$X_{226}$, $X_{333}$, $X_{334}$, $X_{368}$, $X_{369}$, $X_{79a}$, $X_{79b}$, $X_{79c}$, $X_{79d}$, $X_{79e}$, $X_{79f}$, $X_{79g}$, $X_{79h}$, $X_{79i}$, $X_{79j}$ |
| Curves that minimally cover $X_{79}$ and have infinitely many rational
points. |
$X_{226}$, $X_{79a}$, $X_{79b}$, $X_{79c}$, $X_{79d}$, $X_{79e}$, $X_{79f}$, $X_{79g}$, $X_{79h}$, $X_{79i}$, $X_{79j}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{79}) = \mathbb{Q}(f_{79}), f_{32} =
\frac{4f_{79}^{2} - 8}{f_{79}^{2} + 4f_{79} + 2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 117603x - 15523002$, with conductor $10080$ |
| Generic density of odd order reductions |
$289/1792$ |