Curve name  $X_{63}$  
Index  $24$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 2 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{35}$  
Curves that $X_{63}$ minimally covers  $X_{35}$, $X_{39}$, $X_{47}$  
Curves that minimally cover $X_{63}$  $X_{254}$, $X_{263}$, $X_{302}$, $X_{307}$  
Curves that minimally cover $X_{63}$ and have infinitely many rational points.  $X_{302}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{63}) = \mathbb{Q}(f_{63}), f_{35} = \frac{8f_{63}}{f_{63}^{2}  2}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  538x  4628$, with conductor $2400$  
Generic density of odd order reductions  $1343/5376$ 