## The modular curve $X_{335}$

Curve name $X_{335}$
Index $48$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 13 & 13 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $24$ $X_{85}$
Meaning/Special name
Chosen covering $X_{85}$
Curves that $X_{335}$ minimally covers $X_{85}$, $X_{122}$, $X_{168}$
Curves that minimally cover $X_{335}$ $X_{466}$, $X_{473}$, $X_{478}$, $X_{482}$, $X_{560}$, $X_{561}$, $X_{562}$, $X_{567}$, $X_{656}$, $X_{659}$, $X_{660}$, $X_{661}$
Curves that minimally cover $X_{335}$ 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