| Curve name |
$X_{74}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 2 \\ 2 & 3 \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 |
$X_{26}$ |
| Curves that $X_{74}$ minimally covers |
$X_{26}$, $X_{43}$, $X_{47}$ |
| Curves that minimally cover $X_{74}$ |
$X_{275}$, $X_{278}$ |
| Curves that minimally cover $X_{74}$ and have infinitely many rational
points. |
|
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{74}) = \mathbb{Q}(f_{74}), f_{26} =
\frac{f_{74}}{f_{74}^{2} - \frac{1}{4}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 + 572906x - 1075433592$, with conductor $16810$ |
| Generic density of odd order reductions |
$109/448$ |