Curve name  $X_{365}$  
Index  $48$  
Level  $16$  
Genus  $2$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 9 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 10 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 11 & 11 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{124}$  
Curves that $X_{365}$ minimally covers  $X_{124}$, $X_{144}$, $X_{161}$  
Curves that minimally cover $X_{365}$  
Curves that minimally cover $X_{365}$ and have infinitely many rational points.  
Model  A model was not computed. This curve is covered by $X_{53}$, 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 