| Curve name |
$X_{281}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 9 & 2 \\ 2 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 8 & 1 \end{matrix}\right],
\left[ \begin{matrix} 9 & 9 \\ 4 & 3 \end{matrix}\right],
\left[ \begin{matrix} 5 & 15 \\ 4 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{90}$ |
| Curves that $X_{281}$ minimally covers |
$X_{90}$, $X_{107}$, $X_{166}$ |
| Curves that minimally cover $X_{281}$ |
$X_{583}$, $X_{584}$, $X_{641}$, $X_{680}$, $X_{683}$ |
| Curves that minimally cover $X_{281}$ and have infinitely many rational
points. |
|
| Model |
\[y^2 = x^3 + x^2 - 13x - 21\] |
| Info about rational points |
$X_{281}(\mathbb{Q}) \cong \mathbb{Z}/2\mathbb{Z} \times\mathbb{Z}$ |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 14098626487x + 643932904467966$, with conductor $122740$ |
| Generic density of odd order reductions |
$45667/172032$ |