| Curve name |
$X_{187}$ |
| Index |
$48$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 0 \\ 0 & 5 \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 \\ 4 & 5 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 6 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{58}$ |
| Curves that $X_{187}$ minimally covers |
$X_{58}$, $X_{98}$, $X_{99}$ |
| Curves that minimally cover $X_{187}$ |
$X_{449}$, $X_{454}$, $X_{457}$, $X_{459}$, $X_{460}$, $X_{465}$, $X_{187a}$, $X_{187b}$, $X_{187c}$, $X_{187d}$, $X_{187e}$, $X_{187f}$, $X_{187g}$, $X_{187h}$, $X_{187i}$, $X_{187j}$, $X_{187k}$, $X_{187l}$ |
| Curves that minimally cover $X_{187}$ and have infinitely many rational
points. |
$X_{187a}$, $X_{187b}$, $X_{187c}$, $X_{187d}$, $X_{187e}$, $X_{187f}$, $X_{187g}$, $X_{187h}$, $X_{187i}$, $X_{187j}$, $X_{187k}$, $X_{187l}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{187}) = \mathbb{Q}(f_{187}), f_{58} =
\frac{-2}{f_{187}^{2}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - 491x + 1896$, with conductor $735$ |
| Generic density of odd order reductions |
$25/224$ |