| Curve name |
$X_{94}$ |
| 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} 3 & 0 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 4 & 3 \end{matrix}\right],
\left[ \begin{matrix} 5 & 5 \\ 4 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{27}$ |
| Curves that $X_{94}$ minimally covers |
$X_{27}$, $X_{34}$, $X_{45}$ |
| Curves that minimally cover $X_{94}$ |
$X_{231}$, $X_{260}$, $X_{277}$, $X_{376}$, $X_{378}$, $X_{94a}$, $X_{94b}$, $X_{94c}$, $X_{94d}$, $X_{94e}$, $X_{94f}$ |
| Curves that minimally cover $X_{94}$ and have infinitely many rational
points. |
$X_{231}$, $X_{94a}$, $X_{94b}$, $X_{94c}$, $X_{94d}$, $X_{94e}$, $X_{94f}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{94}) = \mathbb{Q}(f_{94}), f_{27} =
\frac{\frac{1}{2}f_{94}^{2} - 4}{f_{94}^{2} + 8f_{94} + 8}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - 5148x - 390528$, with conductor $10080$ |
| Generic density of odd order reductions |
$289/1792$ |