The modular curve $X_{589}$

Curve name	$X_{589}$
Index	$96$
Level	$16$
Genus	$3$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 5 & 10 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 9 & 9 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 8 & 1 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{11}$ $8$ $24$ $X_{91}$
Meaning/Special name
Chosen covering	$X_{287}$
Curves that $X_{589}$ minimally covers	$X_{287}$, $X_{291}$, $X_{352}$
Curves that minimally cover $X_{589}$
Curves that minimally cover $X_{589}$ and have infinitely many rational points.
Model	A model was not computed. This curve is covered by $X_{161}$, 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

Back to the 2-adic image homepage.