The modular curve $X_{469}$

Curve name	$X_{469}$
Index	$96$
Level	$16$
Genus	$1$
Does the subgroup contain $-I$?	Yes
Generating matrices	$\left[ \begin{matrix} 1 & 2 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 5 \end{matrix}\right]$
Images in lower levels	Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$ $8$ $48$ $X_{194}$
Meaning/Special name
Chosen covering	$X_{194}$
Curves that $X_{469}$ minimally covers	$X_{194}$, $X_{215}$, $X_{316}$
Curves that minimally cover $X_{469}$
Curves that minimally cover $X_{469}$ and have infinitely many rational points.
Model	A model was not computed. This curve is covered by $X_{157}$, 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.