## The modular curve $X_{249}$

Curve name $X_{249}$
Index $48$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 4 & 3 \end{matrix}\right]$
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 $X_{249}$ minimally covers $X_{58}$, $X_{96}$, $X_{142}$
Curves that minimally cover $X_{249}$ $X_{452}$, $X_{458}$, $X_{460}$, $X_{465}$, $X_{536}$, $X_{541}$, $X_{586}$, $X_{614}$
Curves that minimally cover $X_{249}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{51}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None