## The modular curve $X_{255}$

Curve name $X_{255}$
Index $48$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 6 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 4 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 4 \\ 0 & 7 \end{matrix}\right]$
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 $X_{255}$ minimally covers $X_{58}$, $X_{64}$, $X_{67}$, $X_{68}$, $X_{127}$, $X_{132}$, $X_{146}$
Curves that minimally cover $X_{255}$ $X_{447}$, $X_{457}$, $X_{541}$
Curves that minimally cover $X_{255}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{54}$, which only has finitely many rational points.
Elliptic curve whose $2$-adic image is the subgroup None