| Curve name |
$X_{203}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 5 & 2 \\ 4 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 4 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{62}$ |
| Curves that $X_{203}$ minimally covers |
$X_{62}$, $X_{99}$, $X_{101}$ |
| Curves that minimally cover $X_{203}$ |
$X_{442}$, $X_{451}$, $X_{462}$, $X_{463}$, $X_{203a}$, $X_{203b}$, $X_{203c}$, $X_{203d}$, $X_{203e}$, $X_{203f}$, $X_{203g}$, $X_{203h}$ |
| Curves that minimally cover $X_{203}$ and have infinitely many rational
points. |
$X_{203a}$, $X_{203b}$, $X_{203c}$, $X_{203d}$, $X_{203e}$, $X_{203f}$, $X_{203g}$, $X_{203h}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{203}) = \mathbb{Q}(f_{203}), f_{62} =
\frac{f_{203}}{f_{203}^{2} + \frac{1}{8}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 15606x + 754272$, with conductor $306$ |
| Generic density of odd order reductions |
$635/5376$ |