| Curve name |
$X_{107}$ |
| Index |
$24$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 5 & 15 \\ 2 & 3 \end{matrix}\right],
\left[ \begin{matrix} 13 & 13 \\ 2 & 3 \end{matrix}\right],
\left[ \begin{matrix} 5 & 10 \\ 2 & 3 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{39}$ |
| Curves that $X_{107}$ minimally covers |
$X_{39}$ |
| Curves that minimally cover $X_{107}$ |
$X_{214}$, $X_{222}$, $X_{224}$, $X_{237}$, $X_{281}$, $X_{287}$, $X_{307}$, $X_{308}$, $X_{362}$, $X_{372}$, $X_{374}$, $X_{399}$ |
| Curves that minimally cover $X_{107}$ and have infinitely many rational
points. |
$X_{214}$, $X_{222}$, $X_{224}$, $X_{237}$, $X_{281}$, $X_{308}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{107}) = \mathbb{Q}(f_{107}), f_{39} =
8f_{107}^{2} - 4\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 22402x + 539748$, with conductor $3038$ |
| Generic density of odd order reductions |
$85091/344064$ |