| Curve name |
$X_{221}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 15 & 14 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 12 & 3 \end{matrix}\right],
\left[ \begin{matrix} 9 & 11 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{95}$ |
| Curves that $X_{221}$ minimally covers |
$X_{95}$, $X_{105}$, $X_{106}$ |
| Curves that minimally cover $X_{221}$ |
$X_{221a}$, $X_{221b}$, $X_{221c}$, $X_{221d}$ |
| Curves that minimally cover $X_{221}$ and have infinitely many rational
points. |
$X_{221a}$, $X_{221b}$, $X_{221c}$, $X_{221d}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{221}) = \mathbb{Q}(f_{221}), f_{95} =
f_{221}^{2}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 6x + 377$, with conductor $153$ |
| Generic density of odd order reductions |
$9249/57344$ |