The modular curve $X_{537}$

Curve name $X_{537}$
Index $96$
Level $8$
Genus $3$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 3 & 7 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $24$ $X_{60}$
Meaning/Special name
Chosen covering $X_{250}$
Curves that $X_{537}$ minimally covers $X_{180}$, $X_{250}$, $X_{253}$, $X_{277}$
Curves that minimally cover $X_{537}$
Curves that minimally cover $X_{537}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{53}$, 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

Back to the 2-adic image homepage.