| Curve name |
$X_{230}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 8 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{102}$ |
| Curves that $X_{230}$ minimally covers |
$X_{102}$, $X_{117}$, $X_{122}$ |
| Curves that minimally cover $X_{230}$ |
$X_{467}$, $X_{473}$, $X_{475}$, $X_{487}$, $X_{230a}$, $X_{230b}$, $X_{230c}$, $X_{230d}$, $X_{230e}$, $X_{230f}$, $X_{230g}$, $X_{230h}$ |
| Curves that minimally cover $X_{230}$ and have infinitely many rational
points. |
$X_{230a}$, $X_{230b}$, $X_{230c}$, $X_{230d}$, $X_{230e}$, $X_{230f}$, $X_{230g}$, $X_{230h}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{230}) = \mathbb{Q}(f_{230}), f_{102} =
-2f_{230}^{2} + 1\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 36x - 176$, with conductor $126$ |
| Generic density of odd order reductions |
$193/1792$ |