| Curve name |
$X_{308}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 9 & 4 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 14 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 15 & 9 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 15 & 14 \\ 2 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{97}$ |
| Curves that $X_{308}$ minimally covers |
$X_{97}$, $X_{107}$, $X_{165}$ |
| Curves that minimally cover $X_{308}$ |
$X_{632}$, $X_{634}$, $X_{672}$, $X_{673}$ |
| Curves that minimally cover $X_{308}$ and have infinitely many rational
points. |
|
| Model |
\[y^2 = x^3 + x^2 - 3x + 1\] |
| Info about rational points |
$X_{308}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$ |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 36892805x + 85720848400$, with conductor $173600$ |
| Generic density of odd order reductions |
$42979/172032$ |