The modular curve $X_{467}$

Curve name	$X_{467}$
Index	$96$
Level	$16$
Genus	$1$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $48$ $X_{197}$
Meaning/Special name
Chosen covering	$X_{197}$
Curves that $X_{467}$ minimally covers	$X_{197}$, $X_{217}$, $X_{229}$, $X_{230}$, $X_{330}$, $X_{337}$, $X_{340}$
Curves that minimally cover $X_{467}$
Curves that minimally cover $X_{467}$ 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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