The modular curve $X_{254}$

Curve name $X_{254}$
Index $48$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 3 & 6 \\ 2 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 6 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $12$ $X_{24}$
Meaning/Special name
Chosen covering $X_{61}$
Curves that $X_{254}$ minimally covers $X_{61}$, $X_{63}$, $X_{66}$, $X_{97}$, $X_{132}$, $X_{143}$, $X_{147}$
Curves that minimally cover $X_{254}$
Curves that minimally cover $X_{254}$ 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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