The modular curve $X_{487}$

Curve name $X_{487}$
Index $96$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{27}$
$8$ $48$ $X_{195}$
Meaning/Special name
Chosen covering $X_{195}$
Curves that $X_{487}$ minimally covers $X_{195}$, $X_{207}$, $X_{228}$, $X_{230}$, $X_{306}$, $X_{346}$, $X_{347}$
Curves that minimally cover $X_{487}$
Curves that minimally cover $X_{487}$ and have infinitely many rational points.
Model A model was not computed. This curve is covered by $X_{159}$, 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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