## The modular curve $X_{251}$

Curve name $X_{251}$
Index $48$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 6 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 4 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{58}$
Meaning/Special name
Chosen covering $X_{58}$
Curves that $X_{251}$ minimally covers $X_{58}$, $X_{61}$, $X_{65}$, $X_{69}$, $X_{136}$, $X_{141}$, $X_{148}$
Curves that minimally cover $X_{251}$ $X_{454}$, $X_{536}$, $X_{540}$, $X_{602}$, $X_{670}$
Curves that minimally cover $X_{251}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{53}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None