Curve name  $X_{699}$  
Index  $96$  
Level  $64$  
Genus  $5$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 7 & 7 \\ 32 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 32 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 32 & 7 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{354}$  
Curves that $X_{699}$ minimally covers  $X_{354}$  
Curves that minimally cover $X_{699}$  
Curves that minimally cover $X_{699}$ and have infinitely many rational points.  
Model  A model was not computed. This curve is covered by $X_{354}$, 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 