The modular curve $X_{147}$

Curve name $X_{147}$
Index $24$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 3 \\ 6 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 4 & 5 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{11}$
Meaning/Special name
Chosen covering $X_{35}$
Curves that $X_{147}$ minimally covers $X_{35}$, $X_{39}$, $X_{54}$
Curves that minimally cover $X_{147}$ $X_{254}$, $X_{261}$, $X_{394}$, $X_{399}$
Curves that minimally cover $X_{147}$ 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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