The modular curve $X_{250}$

Curve name	$X_{250}$
Index	$48$
Level	$8$
Genus	$1$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 1 & 5 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 7 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{23}$
Meaning/Special name
Chosen covering	$X_{69}$
Curves that $X_{250}$ minimally covers	$X_{69}$
Curves that minimally cover $X_{250}$	$X_{537}$, $X_{539}$, $X_{540}$, $X_{542}$, $X_{570}$, $X_{575}$, $X_{577}$, $X_{578}$
Curves that minimally cover $X_{250}$ and have infinitely many rational points.
Model	A model was not computed. This curve does not have local points.
Info about rational points
Comments on finding rational points	None
Elliptic curve whose $2$-adic image is the subgroup	None
Generic density of odd order reductions	N/A

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