The modular curve $X_{400}$

Curve name $X_{400}$
Index $48$
Level $16$
Genus $2$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 7 & 0 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 13 & 13 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 13 & 0 \\ 2 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{23}$
$8$ $24$ $X_{80}$
Meaning/Special name
Chosen covering $X_{80}$
Curves that $X_{400}$ minimally covers $X_{80}$, $X_{161}$, $X_{165}$
Curves that minimally cover $X_{400}$
Curves that minimally cover $X_{400}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{161}$, 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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