| Curve name |
$X_{215}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 8 & 3 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{96}$ |
| Curves that $X_{215}$ minimally covers |
$X_{96}$, $X_{119}$, $X_{120}$ |
| Curves that minimally cover $X_{215}$ |
$X_{469}$, $X_{470}$, $X_{483}$, $X_{485}$, $X_{215a}$, $X_{215b}$, $X_{215c}$, $X_{215d}$, $X_{215e}$, $X_{215f}$, $X_{215g}$, $X_{215h}$, $X_{215i}$, $X_{215j}$, $X_{215k}$, $X_{215l}$ |
| Curves that minimally cover $X_{215}$ and have infinitely many rational
points. |
$X_{215a}$, $X_{215b}$, $X_{215c}$, $X_{215d}$, $X_{215e}$, $X_{215f}$, $X_{215g}$, $X_{215h}$, $X_{215i}$, $X_{215j}$, $X_{215k}$, $X_{215l}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{215}) = \mathbb{Q}(f_{215}), f_{96} =
\frac{2}{f_{215}^{2}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - 246x - 1485$, with conductor $735$ |
| Generic density of odd order reductions |
$25/224$ |