| Curve name |
$X_{100}$ |
| Index |
$24$ |
| Level |
$8$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 4 & 7 \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 $X_{100}$ minimally covers |
$X_{25}$, $X_{33}$, $X_{34}$ |
| Curves that minimally cover $X_{100}$ |
$X_{181}$, $X_{182}$, $X_{188}$, $X_{190}$, $X_{247}$, $X_{248}$, $X_{100a}$, $X_{100b}$, $X_{100c}$, $X_{100d}$, $X_{100e}$, $X_{100f}$, $X_{100g}$, $X_{100h}$, $X_{100i}$, $X_{100j}$ |
| Curves that minimally cover $X_{100}$ and have infinitely many rational
points. |
$X_{181}$, $X_{188}$, $X_{190}$, $X_{100a}$, $X_{100b}$, $X_{100c}$, $X_{100d}$, $X_{100e}$, $X_{100f}$, $X_{100g}$, $X_{100h}$, $X_{100i}$, $X_{100j}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{100}) = \mathbb{Q}(f_{100}), f_{25} =
\frac{2}{f_{100}^{2}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 18759x - 980390$, with conductor $5544$ |
| Generic density of odd order reductions |
$643/5376$ |