Curve name  $X_{200}$  
Index  $48$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 4 & 7 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{62}$  
Curves that $X_{200}$ minimally covers  $X_{62}$, $X_{98}$, $X_{101}$  
Curves that minimally cover $X_{200}$  $X_{451}$, $X_{455}$, $X_{456}$, $X_{462}$, $X_{200a}$, $X_{200b}$, $X_{200c}$, $X_{200d}$, $X_{200e}$, $X_{200f}$, $X_{200g}$, $X_{200h}$  
Curves that minimally cover $X_{200}$ and have infinitely many rational points.  $X_{200a}$, $X_{200b}$, $X_{200c}$, $X_{200d}$, $X_{200e}$, $X_{200f}$, $X_{200g}$, $X_{200h}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{200}) = \mathbb{Q}(f_{200}), f_{62} = \frac{f_{200}^{2}  \frac{1}{2}}{f_{200}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2  936x  3668$, with conductor $126$  
Generic density of odd order reductions  $193/1792$ 