| Curve name |
$X_{237}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 11 & 11 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 14 \\ 2 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{83}$ |
| Curves that $X_{237}$ minimally covers |
$X_{83}$, $X_{106}$, $X_{107}$ |
| Curves that minimally cover $X_{237}$ |
|
| Curves that minimally cover $X_{237}$ and have infinitely many rational
points. |
|
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{237}) = \mathbb{Q}(f_{237}), f_{83} =
\frac{f_{237}}{f_{237}^{2} + 2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 221950x + 40248384$, with conductor $147712$ |
| Generic density of odd order reductions |
$45667/172032$ |