| Curve name |
$X_{210}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 2 \\ 14 & 5 \end{matrix}\right],
\left[ \begin{matrix} 3 & 6 \\ 10 & 5 \end{matrix}\right],
\left[ \begin{matrix} 1 & 2 \\ 14 & 1 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{61}$ |
| Curves that $X_{210}$ minimally covers |
$X_{61}$, $X_{111}$, $X_{112}$ |
| Curves that minimally cover $X_{210}$ |
$X_{210a}$, $X_{210b}$, $X_{210c}$, $X_{210d}$ |
| Curves that minimally cover $X_{210}$ and have infinitely many rational
points. |
$X_{210a}$, $X_{210b}$, $X_{210c}$, $X_{210d}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{210}) = \mathbb{Q}(f_{210}), f_{61} =
\frac{2}{f_{210}^{2}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 51x + 152$, with conductor $153$ |
| Generic density of odd order reductions |
$9249/57344$ |