| Curve name |
$X_{235}$ |
| Index |
$48$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right],
\left[ \begin{matrix} 7 & 0 \\ 0 & 15 \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 |
$X_{102}$ |
| Curves that $X_{235}$ minimally covers |
$X_{102}$, $X_{118}$, $X_{120}$ |
| Curves that minimally cover $X_{235}$ |
$X_{470}$, $X_{471}$, $X_{479}$, $X_{481}$, $X_{496}$, $X_{499}$, $X_{515}$, $X_{516}$, $X_{517}$, $X_{518}$, $X_{523}$, $X_{524}$, $X_{534}$, $X_{535}$, $X_{235a}$, $X_{235b}$, $X_{235c}$, $X_{235d}$, $X_{235e}$, $X_{235f}$, $X_{235g}$, $X_{235h}$, $X_{235i}$, $X_{235j}$, $X_{235k}$, $X_{235l}$, $X_{235m}$, $X_{235n}$, $X_{235o}$, $X_{235p}$, $X_{235q}$, $X_{235r}$, $X_{235s}$, $X_{235t}$ |
| Curves that minimally cover $X_{235}$ and have infinitely many rational
points. |
$X_{235a}$, $X_{235b}$, $X_{235c}$, $X_{235d}$, $X_{235e}$, $X_{235f}$, $X_{235g}$, $X_{235h}$, $X_{235i}$, $X_{235j}$, $X_{235k}$, $X_{235l}$, $X_{235m}$, $X_{235n}$, $X_{235o}$, $X_{235p}$, $X_{235q}$, $X_{235r}$, $X_{235s}$, $X_{235t}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{235}) = \mathbb{Q}(f_{235}), f_{102} =
-f_{235}^{2} + 1\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy + y = x^3 + 25407x - 1172492$, with conductor $25410$ |
| Generic density of odd order reductions |
$17/168$ |