Curve name  $X_{35}$  
Index  $12$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 6 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 5 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{11}$  
Curves that $X_{35}$ minimally covers  $X_{11}$  
Curves that minimally cover $X_{35}$  $X_{61}$, $X_{63}$, $X_{65}$, $X_{82}$, $X_{147}$, $X_{148}$  
Curves that minimally cover $X_{35}$ and have infinitely many rational points.  $X_{61}$, $X_{63}$, $X_{65}$, $X_{82}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{35}) = \mathbb{Q}(f_{35}), f_{11} = f_{35}^{2} + 8\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  333x + 2088$, with conductor $300$  
Generic density of odd order reductions  $2659/10752$ 