| Curve name |
$X_{183}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 0 \\ 6 & 3 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 3 & 4 \\ 6 & 5 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{58}$ |
| Curves that $X_{183}$ minimally covers |
$X_{58}$, $X_{87}$, $X_{101}$ |
| Curves that minimally cover $X_{183}$ |
$X_{446}$, $X_{447}$, $X_{450}$, $X_{452}$, $X_{454}$, $X_{458}$, $X_{183a}$, $X_{183b}$, $X_{183c}$, $X_{183d}$, $X_{183e}$, $X_{183f}$, $X_{183g}$, $X_{183h}$, $X_{183i}$, $X_{183j}$, $X_{183k}$, $X_{183l}$ |
| Curves that minimally cover $X_{183}$ and have infinitely many rational
points. |
$X_{183a}$, $X_{183b}$, $X_{183c}$, $X_{183d}$, $X_{183e}$, $X_{183f}$, $X_{183g}$, $X_{183h}$, $X_{183i}$, $X_{183j}$, $X_{183k}$, $X_{183l}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{183}) = \mathbb{Q}(f_{183}), f_{58} =
-f_{183}^{2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 12960x - 453200$, with conductor $1530$ |
| Generic density of odd order reductions |
$25/224$ |