| Curve name |
$X_{208}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 0 \\ 8 & 7 \end{matrix}\right],
\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 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{96}$ |
| Curves that $X_{208}$ minimally covers |
$X_{96}$, $X_{121}$, $X_{122}$ |
| Curves that minimally cover $X_{208}$ |
$X_{468}$, $X_{475}$, $X_{482}$, $X_{486}$, $X_{208a}$, $X_{208b}$, $X_{208c}$, $X_{208d}$, $X_{208e}$, $X_{208f}$, $X_{208g}$, $X_{208h}$, $X_{208i}$, $X_{208j}$, $X_{208k}$, $X_{208l}$ |
| Curves that minimally cover $X_{208}$ and have infinitely many rational
points. |
$X_{208a}$, $X_{208b}$, $X_{208c}$, $X_{208d}$, $X_{208e}$, $X_{208f}$, $X_{208g}$, $X_{208h}$, $X_{208i}$, $X_{208j}$, $X_{208k}$, $X_{208l}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{208}) = \mathbb{Q}(f_{208}), f_{96} =
f_{208}^{2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 12240x - 518144$, with conductor $1530$ |
| Generic density of odd order reductions |
$25/224$ |