The modular curve $X_{444}$

Curve name $X_{444}$
Index $96$
Level $8$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $24$ $X_{60}$
Meaning/Special name
Chosen covering $X_{196}$
Curves that $X_{444}$ minimally covers $X_{196}$, $X_{205}$, $X_{278}$
Curves that minimally cover $X_{444}$
Curves that minimally cover $X_{444}$ 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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