| Curve name |
$X_{119}$ |
| Index |
$24$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 3 \\ 0 & 3 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 8 & 3 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{36}$ |
| Curves that $X_{119}$ minimally covers |
$X_{36}$ |
| Curves that minimally cover $X_{119}$ |
$X_{213}$, $X_{215}$, $X_{219}$, $X_{233}$, $X_{338}$, $X_{344}$, $X_{119a}$, $X_{119b}$, $X_{119c}$, $X_{119d}$, $X_{119e}$, $X_{119f}$, $X_{119g}$, $X_{119h}$, $X_{119i}$, $X_{119j}$, $X_{119k}$, $X_{119l}$, $X_{119m}$, $X_{119n}$, $X_{119o}$, $X_{119p}$ |
| Curves that minimally cover $X_{119}$ and have infinitely many rational
points. |
$X_{213}$, $X_{215}$, $X_{219}$, $X_{233}$, $X_{119a}$, $X_{119b}$, $X_{119c}$, $X_{119d}$, $X_{119e}$, $X_{119f}$, $X_{119g}$, $X_{119h}$, $X_{119i}$, $X_{119j}$, $X_{119k}$, $X_{119l}$, $X_{119m}$, $X_{119n}$, $X_{119o}$, $X_{119p}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{119}) = \mathbb{Q}(f_{119}), f_{36} =
-f_{119}^{2} - 4\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 - x^2 - 4851x - 128840$, with conductor $1989$ |
| Generic density of odd order reductions |
$83/672$ |