## The modular curve $X_{235}$

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
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{102}$
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 $\mathbb{P}^{1}, \mathbb{Q}(X_{235}) = \mathbb{Q}(f_{235}), f_{102} = -f_{235}^{2} + 1$
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 $17/168$