| Curve name |
$X_{302}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 13 & 7 \\ 2 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 2 & 1 \end{matrix}\right],
\left[ \begin{matrix} 13 & 10 \\ 2 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{63}$ |
| Curves that $X_{302}$ minimally covers |
$X_{63}$, $X_{105}$, $X_{166}$ |
| Curves that minimally cover $X_{302}$ |
|
| Curves that minimally cover $X_{302}$ and have infinitely many rational
points. |
|
| Model |
\[y^2 = x^3 + x^2 - 13x - 21\] |
| Info about rational points |
$X_{302}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$ |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 + x^2 - 7859386910x - 268185327947856$, with conductor
$30631008$ |
| Generic density of odd order reductions |
$42979/172032$ |