The modular curve $X_{72}$

Curve name	$X_{72}$
Index	$24$
Level	$8$
Genus	$0$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 3 & 6 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 3 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{12}$
Meaning/Special name
Chosen covering	$X_{30}$
Curves that $X_{72}$ minimally covers	$X_{30}$
Curves that minimally cover $X_{72}$	$X_{266}$, $X_{273}$
Curves that minimally cover $X_{72}$ and have infinitely many rational points.
Model	A model was not computed. This curve is a conic with no 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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