## The modular curve $X_{316}$

Curve name $X_{316}$
Index $48$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$ $8$ $24$ $X_{96}$
Meaning/Special name
Chosen covering $X_{96}$
Curves that $X_{316}$ minimally covers $X_{96}$, $X_{116}$, $X_{157}$
Curves that minimally cover $X_{316}$ $X_{469}$, $X_{486}$, $X_{586}$, $X_{613}$, $X_{624}$, $X_{625}$, $X_{681}$, $X_{682}$
Curves that minimally cover $X_{316}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{157}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None