The modular curve $X_{719}$

Curve name	$X_{719}$
Index	$128$
Level	$32$
Genus	$5$
Does the subgroup contain $-I$?	Yes
Generating matrices	$ \left[ \begin{matrix} 4 & 1 \\ 1 & 4 \end{matrix}\right], \left[ \begin{matrix} 2 & 3 \\ 1 & 7 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $1$ $X_{1}$ $4$ $4$ $X_{7}$ $8$ $32$ $X_{179}$ $16$ $64$ $X_{439}$
Meaning/Special name
Chosen covering	$X_{439}$
Curves that $X_{719}$ minimally covers	$X_{177}$, $X_{439}$
Curves that minimally cover $X_{719}$
Curves that minimally cover $X_{719}$ and have infinitely many rational points.
Model	A model was not computed. This curve is covered by $X_{179}$, which only has finitely many rational 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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