The modular curve $X_{585}$

Curve name $X_{585}$
Index $96$
Level $16$
Genus $3$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 5 & 10 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 11 & 11 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 9 & 9 \\ 2 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{11}$
$8$ $24$ $X_{91}$
Meaning/Special name
Chosen covering $X_{289}$
Curves that $X_{585}$ minimally covers $X_{289}$, $X_{291}$, $X_{352}$
Curves that minimally cover $X_{585}$
Curves that minimally cover $X_{585}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{352}$, 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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