## The modular curve $X_{340}$

Curve name $X_{340}$
Index $48$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 10 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right]$
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 $X_{340}$ minimally covers $X_{102}$, $X_{120}$, $X_{168}$
Curves that minimally cover $X_{340}$ $X_{467}$, $X_{470}$, $X_{474}$, $X_{479}$, $X_{552}$, $X_{553}$, $X_{554}$, $X_{559}$, $X_{639}$, $X_{642}$, $X_{644}$, $X_{648}$
Curves that minimally cover $X_{340}$ 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