| Curve name |
$X_{181}$ |
| 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} 7 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 2 \\ 0 & 5 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{87}$ |
| Curves that $X_{181}$ minimally covers |
$X_{87}$, $X_{98}$, $X_{100}$ |
| Curves that minimally cover $X_{181}$ |
$X_{448}$, $X_{450}$, $X_{455}$, $X_{459}$, $X_{181a}$, $X_{181b}$, $X_{181c}$, $X_{181d}$, $X_{181e}$, $X_{181f}$, $X_{181g}$, $X_{181h}$ |
| Curves that minimally cover $X_{181}$ and have infinitely many rational
points. |
$X_{181a}$, $X_{181b}$, $X_{181c}$, $X_{181d}$, $X_{181e}$, $X_{181f}$, $X_{181g}$, $X_{181h}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{181}) = \mathbb{Q}(f_{181}), f_{87} =
\frac{f_{181}^{2} - \frac{1}{8}}{f_{181}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 1026x + 10692$, with conductor $306$ |
| Generic density of odd order reductions |
$635/5376$ |