The modular curve $X_{322}$

Curve name	$X_{322}$
Index	$48$
Level	$16$
Genus	$1$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 13 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 13 & 13 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 4 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{23}$ $8$ $24$ $X_{69}$
Meaning/Special name
Chosen covering	$X_{69}$
Curves that $X_{322}$ minimally covers	$X_{69}$, $X_{111}$, $X_{149}$
Curves that minimally cover $X_{322}$	$X_{569}$, $X_{577}$
Curves that minimally cover $X_{322}$ and have infinitely many rational points.
Model	A model was not computed. This curve is covered by $X_{149}$, 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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