The modular curve $X_{276}$

Curve name $X_{276}$
Index $48$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 7 & 3 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 2 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 4 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{26}$
Meaning/Special name
Chosen covering $X_{73}$
Curves that $X_{276}$ minimally covers $X_{73}$, $X_{77}$, $X_{83}$, $X_{91}$, $X_{125}$, $X_{139}$, $X_{143}$
Curves that minimally cover $X_{276}$ $X_{484}$, $X_{538}$, $X_{598}$
Curves that minimally cover $X_{276}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{54}$, 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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