Curve name  $X_{45}$  
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} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 5 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 5 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{11}$  
Curves that $X_{45}$ minimally covers  $X_{11}$  
Curves that minimally cover $X_{45}$  $X_{61}$, $X_{69}$, $X_{70}$, $X_{73}$, $X_{77}$, $X_{81}$, $X_{94}$, $X_{97}$, $X_{109}$, $X_{110}$, $X_{111}$, $X_{112}$, $X_{130}$, $X_{136}$, $X_{140}$, $X_{143}$, $X_{149}$, $X_{150}$, $X_{151}$, $X_{153}$  
Curves that minimally cover $X_{45}$ and have infinitely many rational points.  $X_{61}$, $X_{69}$, $X_{70}$, $X_{73}$, $X_{77}$, $X_{81}$, $X_{94}$, $X_{97}$, $X_{109}$, $X_{110}$, $X_{111}$, $X_{112}$, $X_{150}$, $X_{153}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{45}) = \mathbb{Q}(f_{45}), f_{11} = f_{45}^{2} + 8\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2 + 258x + 1791$, with conductor $1575$  
Generic density of odd order reductions  $2659/10752$ 