The modular curve $X_{596}$

Curve name $X_{596}$
Index $96$
Level $16$
Genus $3$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 6 \\ 2 & 11 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 12 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 7 \\ 10 & 15 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{26}$
$8$ $48$ $X_{253}$
Meaning/Special name
Chosen covering $X_{253}$
Curves that $X_{596}$ minimally covers $X_{253}$, $X_{348}$, $X_{351}$
Curves that minimally cover $X_{596}$
Curves that minimally cover $X_{596}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{149}$, 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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