The modular curve $X_{416}$

Curve name $X_{416}$
Index $48$
Level $16$
Genus $3$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 15 & 13 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 11 & 6 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 9 & 2 \\ 4 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{11}$
$8$ $24$ $X_{131}$
Meaning/Special name
Chosen covering $X_{131}$
Curves that $X_{416}$ minimally covers $X_{131}$, $X_{152}$, $X_{154}$
Curves that minimally cover $X_{416}$
Curves that minimally cover $X_{416}$ 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

Back to the 2-adic image homepage.