| Curve name |
$X_{126}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$1$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 1 \\ 6 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 6 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{30}$ |
| Curves that $X_{126}$ minimally covers |
$X_{30}$, $X_{40}$, $X_{52}$ |
| Curves that minimally cover $X_{126}$ |
$X_{265}$, $X_{266}$, $X_{419}$, $X_{420}$ |
| Curves that minimally cover $X_{126}$ and have infinitely many rational
points. |
|
| Model |
A model was not computed. This curve is covered by $X_{52}$, which only has finitely many rational points. |
| Info about rational points |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
None |
| Generic density of odd order reductions |
N/A |