The modular curve $X_{138}$

Curve name $X_{138}$
Index $24$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{11}$
Meaning/Special name
Chosen covering $X_{41}$
Curves that $X_{138}$ minimally covers $X_{41}$, $X_{47}$, $X_{53}$
Curves that minimally cover $X_{138}$ $X_{263}$, $X_{264}$
Curves that minimally cover $X_{138}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{53}$, 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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