The modular curve $X_{474}$

Curve name $X_{474}$
Index $96$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $48$ $X_{202}$
Meaning/Special name
Chosen covering $X_{202}$
Curves that $X_{474}$ minimally covers $X_{202}$, $X_{223}$, $X_{234}$, $X_{236}$, $X_{332}$, $X_{339}$, $X_{340}$
Curves that minimally cover $X_{474}$
Curves that minimally cover $X_{474}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{168}$, 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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