| Curve name |
$X_{108}$ |
| Index |
$24$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 0 \\ 0 & 11 \end{matrix}\right],
\left[ \begin{matrix} 1 & 1 \\ 10 & 5 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 14 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{42}$ |
| Curves that $X_{108}$ minimally covers |
$X_{42}$ |
| Curves that minimally cover $X_{108}$ |
$X_{238}$, $X_{108a}$, $X_{108b}$, $X_{108c}$, $X_{108d}$, $X_{108e}$, $X_{108f}$ |
| Curves that minimally cover $X_{108}$ and have infinitely many rational
points. |
$X_{238}$, $X_{108a}$, $X_{108b}$, $X_{108c}$, $X_{108d}$, $X_{108e}$, $X_{108f}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{108}) = \mathbb{Q}(f_{108}), f_{42} =
\frac{8f_{108} + 8}{f_{108}^{2} - 2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 = x^3 - x^2 - 31x - 8169$, with conductor $10880$ |
| Generic density of odd order reductions |
$85091/344064$ |