| Curve name |
$X_{92}$ |
| 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} 5 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{27}$ |
| Curves that $X_{92}$ minimally covers |
$X_{27}$, $X_{36}$, $X_{43}$ |
| Curves that minimally cover $X_{92}$ |
$X_{195}$, $X_{205}$, $X_{207}$, $X_{259}$, $X_{278}$, $X_{305}$, $X_{306}$, $X_{371}$, $X_{92a}$, $X_{92b}$, $X_{92c}$, $X_{92d}$, $X_{92e}$, $X_{92f}$, $X_{92g}$, $X_{92h}$, $X_{92i}$, $X_{92j}$, $X_{92k}$ |
| Curves that minimally cover $X_{92}$ and have infinitely many rational
points. |
$X_{195}$, $X_{205}$, $X_{207}$, $X_{92a}$, $X_{92b}$, $X_{92c}$, $X_{92d}$, $X_{92e}$, $X_{92f}$, $X_{92g}$, $X_{92h}$, $X_{92i}$, $X_{92j}$, $X_{92k}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{92}) = \mathbb{Q}(f_{92}), f_{27} =
\frac{f_{92}}{f_{92}^{2} - 1}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 + 33729345x - 401153583974$, with conductor
$6435$ |
| Generic density of odd order reductions |
$19/168$ |