| Curve name |
$X_{120}$ |
| 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} 5 & 0 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{36}$ |
| Curves that $X_{120}$ minimally covers |
$X_{36}$ |
| Curves that minimally cover $X_{120}$ |
$X_{207}$, $X_{215}$, $X_{217}$, $X_{227}$, $X_{229}$, $X_{234}$, $X_{235}$, $X_{236}$, $X_{336}$, $X_{340}$, $X_{341}$, $X_{345}$, $X_{120a}$, $X_{120b}$, $X_{120c}$, $X_{120d}$, $X_{120e}$, $X_{120f}$, $X_{120g}$, $X_{120h}$, $X_{120i}$, $X_{120j}$, $X_{120k}$, $X_{120l}$, $X_{120m}$, $X_{120n}$, $X_{120o}$, $X_{120p}$ |
| Curves that minimally cover $X_{120}$ and have infinitely many rational
points. |
$X_{207}$, $X_{215}$, $X_{217}$, $X_{227}$, $X_{229}$, $X_{234}$, $X_{235}$, $X_{236}$, $X_{120a}$, $X_{120b}$, $X_{120c}$, $X_{120d}$, $X_{120e}$, $X_{120f}$, $X_{120g}$, $X_{120h}$, $X_{120i}$, $X_{120j}$, $X_{120k}$, $X_{120l}$, $X_{120m}$, $X_{120n}$, $X_{120o}$, $X_{120p}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{120}) = \mathbb{Q}(f_{120}), f_{36} =
f_{120}^{2} - 4\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 + x^2 + 25x$, with conductor $525$ |
| Generic density of odd order reductions |
$19/168$ |