| Curve name |
$X_{232}$ |
| 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} 1 & 0 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 10 \\ 2 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{83}$ |
| Curves that $X_{232}$ minimally covers |
$X_{83}$, $X_{105}$, $X_{124}$ |
| Curves that minimally cover $X_{232}$ |
|
| Curves that minimally cover $X_{232}$ and have infinitely many rational
points. |
|
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{232}) = \mathbb{Q}(f_{232}), f_{83} =
\frac{\frac{1}{4}f_{232}^{2} + f_{232} - 1}{f_{232}^{2} + 4}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 760x + 8448$, with conductor $4352$ |
| Generic density of odd order reductions |
$45667/172032$ |