| Curve name |
$X_{238}$ |
| Index |
$48$ |
| Level |
$32$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 21 & 0 \\ 2 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 17 & 19 \\ 2 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{108}$ |
| Curves that $X_{238}$ minimally covers |
$X_{108}$ |
| Curves that minimally cover $X_{238}$ |
$X_{238a}$, $X_{238b}$, $X_{238c}$, $X_{238d}$ |
| Curves that minimally cover $X_{238}$ and have infinitely many rational
points. |
$X_{238a}$, $X_{238b}$, $X_{238c}$, $X_{238d}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{238}) = \mathbb{Q}(f_{238}), f_{108} =
\frac{f_{238}^{2} - f_{238} - \frac{1}{4}}{f_{238}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 + 6x + 20$, with conductor $1152$ |
| Generic density of odd order reductions |
$2722915/11010048$ |