Curve name  $X_{335}$  
Index  $48$  
Level  $16$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 13 & 13 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 15 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{85}$  
Curves that $X_{335}$ minimally covers  $X_{85}$, $X_{122}$, $X_{168}$  
Curves that minimally cover $X_{335}$  $X_{466}$, $X_{473}$, $X_{478}$, $X_{482}$, $X_{560}$, $X_{561}$, $X_{562}$, $X_{567}$, $X_{656}$, $X_{659}$, $X_{660}$, $X_{661}$  
Curves that minimally cover $X_{335}$ and have infinitely many rational points.  
Model  A model was not computed. This curve is covered by $X_{168}$, 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 