| Curve name |
$X_{368}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$2$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 9 & 9 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 11 & 1 \\ 12 & 3 \end{matrix}\right],
\left[ \begin{matrix} 15 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{79}$ |
| Curves that $X_{368}$ minimally covers |
$X_{79}$ |
| Curves that minimally cover $X_{368}$ |
|
| Curves that minimally cover $X_{368}$ and have infinitely many rational
points. |
|
| Model |
\[y^2 = -x^6 + 5x^4 + 5x^2 - 1\] |
| Info about rational points |
No non-singular rational points |
| Comments on finding rational points |
The rank of the Jacobian is 0. We use the method of Chabauty. |
| Elliptic curve whose $2$-adic image is the subgroup |
None |
| Generic density of odd order reductions |
N/A |