Curve name  $X_{251}$  
Index  $48$  
Level  $8$  
Genus  $1$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 7 & 0 \\ 6 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 4 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 4 \\ 0 & 7 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{58}$  
Curves that $X_{251}$ minimally covers  $X_{58}$, $X_{61}$, $X_{65}$, $X_{69}$, $X_{136}$, $X_{141}$, $X_{148}$  
Curves that minimally cover $X_{251}$  $X_{454}$, $X_{536}$, $X_{540}$, $X_{602}$, $X_{670}$  
Curves that minimally cover $X_{251}$ 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 