## The modular curve $X_{496}$

Curve name $X_{496}$
Index $96$
Level $32$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 15 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{102}$ $16$ $48$ $X_{235}$
Meaning/Special name
Chosen covering $X_{235}$
Curves that $X_{496}$ minimally covers $X_{235}$, $X_{240}$, $X_{354}$
Curves that minimally cover $X_{496}$ $X_{722}$, $X_{723}$, $X_{724}$, $X_{725}$
Curves that minimally cover $X_{496}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{354}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None