| Curve name |
$X_{101}$ |
| 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} 7 & 0 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 4 & 7 \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 $X_{101}$ minimally covers |
$X_{25}$ |
| Curves that minimally cover $X_{101}$ |
$X_{183}$, $X_{185}$, $X_{188}$, $X_{189}$, $X_{190}$, $X_{192}$, $X_{200}$, $X_{203}$, $X_{245}$, $X_{268}$, $X_{274}$, $X_{279}$, $X_{101a}$, $X_{101b}$, $X_{101c}$, $X_{101d}$, $X_{101e}$, $X_{101f}$, $X_{101g}$, $X_{101h}$, $X_{101i}$, $X_{101j}$, $X_{101k}$, $X_{101l}$, $X_{101m}$, $X_{101n}$, $X_{101o}$, $X_{101p}$ |
| Curves that minimally cover $X_{101}$ and have infinitely many rational
points. |
$X_{183}$, $X_{185}$, $X_{188}$, $X_{189}$, $X_{190}$, $X_{192}$, $X_{200}$, $X_{203}$, $X_{101a}$, $X_{101b}$, $X_{101c}$, $X_{101d}$, $X_{101e}$, $X_{101f}$, $X_{101g}$, $X_{101h}$, $X_{101i}$, $X_{101j}$, $X_{101k}$, $X_{101l}$, $X_{101m}$, $X_{101n}$, $X_{101o}$, $X_{101p}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{101}) = \mathbb{Q}(f_{101}), f_{25} =
8f_{101}^{2} - 1\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 + x^2 - 1225x - 17000$, with conductor $525$ |
| Generic density of odd order reductions |
$19/168$ |