| Curve name |
$X_{228}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 5 & 5 \\ 0 & 5 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 8 & 3 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{84}$ |
| Curves that $X_{228}$ minimally covers |
$X_{84}$, $X_{117}$, $X_{122}$ |
| Curves that minimally cover $X_{228}$ |
$X_{466}$, $X_{487}$, $X_{228a}$, $X_{228b}$, $X_{228c}$, $X_{228d}$, $X_{228e}$, $X_{228f}$, $X_{228g}$, $X_{228h}$ |
| Curves that minimally cover $X_{228}$ and have infinitely many rational
points. |
$X_{228a}$, $X_{228b}$, $X_{228c}$, $X_{228d}$, $X_{228e}$, $X_{228f}$, $X_{228g}$, $X_{228h}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{228}) = \mathbb{Q}(f_{228}), f_{84} =
\frac{f_{228}^{2} - 8}{f_{228}^{2} + 8f_{228} + 8}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 + x^2 + 17x + 38$, with conductor $600$ |
| Generic density of odd order reductions |
$635/5376$ |