The modular curve $X_{290}$

Curve name $X_{290}$
Index $48$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 9 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 13 & 10 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 5 \\ 8 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{11}$
$8$ $24$ $X_{91}$
Meaning/Special name
Chosen covering $X_{91}$
Curves that $X_{290}$ minimally covers $X_{91}$, $X_{113}$, $X_{152}$
Curves that minimally cover $X_{290}$ $X_{582}$, $X_{587}$, $X_{588}$, $X_{590}$
Curves that minimally cover $X_{290}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{152}$, 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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