| Curve name |
$X_{326}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 15 & 13 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}\right],
\left[ \begin{matrix} 13 & 10 \\ 4 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{70}$ |
| Curves that $X_{326}$ minimally covers |
$X_{70}$, $X_{112}$, $X_{153}$ |
| Curves that minimally cover $X_{326}$ |
|
| Curves that minimally cover $X_{326}$ and have infinitely many rational
points. |
|
| Model |
\[y^2 = x^3 + x^2 - 13x - 21\] |
| Info about rational points |
$X_{326}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$ |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - x^2 - 7802175025x + 272281984973281$, with conductor
$30631008$ |
| Generic density of odd order reductions |
$42979/172032$ |