The modular curve $X_{269}$

Curve name $X_{269}$
Index $48$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{87}$
Curves that $X_{269}$ minimally covers $X_{87}$, $X_{98}$, $X_{129}$
Curves that minimally cover $X_{269}$ $X_{450}$, $X_{456}$, $X_{459}$, $X_{464}$
Curves that minimally cover $X_{269}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{52}$, 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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