The modular curve $X_{348}$

Curve name	$X_{348}$
Index	$48$
Level	$16$
Genus	$1$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 1 & 3 \\ 10 & 15 \end{matrix}\right], \left[ \begin{matrix} 1 & 6 \\ 2 & 11 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 14 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 2 & 11 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{26}$ $8$ $24$ $X_{73}$
Meaning/Special name
Chosen covering	$X_{73}$
Curves that $X_{348}$ minimally covers	$X_{73}$, $X_{113}$, $X_{154}$
Curves that minimally cover $X_{348}$	$X_{594}$, $X_{596}$
Curves that minimally cover $X_{348}$ and have infinitely many rational points.
Model	A model was not computed. This curve is covered by $X_{154}$, 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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