## The modular curve $X_{470}$

Curve name $X_{470}$
Index $96$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 15 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 0 & 9 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 9 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$ $8$ $48$ $X_{193}$
Meaning/Special name
Chosen covering $X_{193}$
Curves that $X_{470}$ minimally covers $X_{193}$, $X_{213}$, $X_{215}$, $X_{235}$, $X_{313}$, $X_{338}$, $X_{340}$
Curves that minimally cover $X_{470}$
Curves that minimally cover $X_{470}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{168}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None