The modular curve $X_{724}$

Curve name $X_{724}$
Index $192$
Level $64$
Genus $5$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 15 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 32 & 9 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{102}$
$16$ $48$ $X_{235}$
$32$ $96$ $X_{496}$
Meaning/Special name
Chosen covering $X_{496}$
Curves that $X_{724}$ minimally covers $X_{496}$
Curves that minimally cover $X_{724}$
Curves that minimally cover $X_{724}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{354}$, 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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