| Curve name |
$X_{98}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 4 & 3 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 4 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{25}$ |
| Curves that $X_{98}$ minimally covers |
$X_{25}$ |
| Curves that minimally cover $X_{98}$ |
$X_{181}$, $X_{187}$, $X_{188}$, $X_{189}$, $X_{193}$, $X_{194}$, $X_{200}$, $X_{204}$, $X_{244}$, $X_{269}$, $X_{272}$, $X_{279}$, $X_{98a}$, $X_{98b}$, $X_{98c}$, $X_{98d}$, $X_{98e}$, $X_{98f}$, $X_{98g}$, $X_{98h}$, $X_{98i}$, $X_{98j}$, $X_{98k}$, $X_{98l}$, $X_{98m}$, $X_{98n}$, $X_{98o}$, $X_{98p}$ |
| Curves that minimally cover $X_{98}$ and have infinitely many rational
points. |
$X_{181}$, $X_{187}$, $X_{188}$, $X_{189}$, $X_{193}$, $X_{194}$, $X_{200}$, $X_{204}$, $X_{98a}$, $X_{98b}$, $X_{98c}$, $X_{98d}$, $X_{98e}$, $X_{98f}$, $X_{98g}$, $X_{98h}$, $X_{98i}$, $X_{98j}$, $X_{98k}$, $X_{98l}$, $X_{98m}$, $X_{98n}$, $X_{98o}$, $X_{98p}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{98}) = \mathbb{Q}(f_{98}), f_{25} =
f_{98}^{2} - 1\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 + x^2 - 100x - 125$, with conductor $525$ |
| Generic density of odd order reductions |
$19/168$ |