Curve name  $X_{49}$  
Index  $12$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 1 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{11}$  
Curves that $X_{49}$ minimally covers  $X_{11}$  
Curves that minimally cover $X_{49}$  $X_{70}$, $X_{71}$, $X_{76}$, $X_{95}$, $X_{130}$, $X_{137}$  
Curves that minimally cover $X_{49}$ and have infinitely many rational points.  $X_{70}$, $X_{71}$, $X_{76}$, $X_{95}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{49}) = \mathbb{Q}(f_{49}), f_{11} = \frac{64}{f_{49}^{2} + 8}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2 + 292x + 9588$, with conductor $300$  
Generic density of odd order reductions  $2659/10752$ 