The modular curve $X_{342}$

Curve name $X_{342}$
Index $48$
Level $16$
Genus $1$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{102}$
Meaning/Special name
Chosen covering $X_{102}$
Curves that $X_{342}$ minimally covers $X_{102}$, $X_{121}$, $X_{159}$
Curves that minimally cover $X_{342}$ $X_{471}$, $X_{475}$
Curves that minimally cover $X_{342}$ 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

Back to the 2-adic image homepage.