The modular curve $X_{21}$

Curve name $X_{21}$
Index $8$
Level $4$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 3 & 0 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $2$ $X_{2}$
Meaning/Special name $X_{ns}(4)$
Chosen covering $X_{7}$
Curves that $X_{21}$ minimally covers $X_{2}$, $X_{7}$
Curves that minimally cover $X_{21}$ $X_{59}$
Curves that minimally cover $X_{21}$ 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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