Curve name  $X_{202}$  
Index  $48$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{78}$  
Curves that $X_{202}$ minimally covers  $X_{78}$, $X_{85}$, $X_{102}$  
Curves that minimally cover $X_{202}$  $X_{471}$, $X_{472}$, $X_{473}$, $X_{474}$, $X_{202a}$, $X_{202b}$, $X_{202c}$, $X_{202d}$, $X_{202e}$, $X_{202f}$, $X_{202g}$, $X_{202h}$  
Curves that minimally cover $X_{202}$ and have infinitely many rational points.  $X_{202a}$, $X_{202b}$, $X_{202c}$, $X_{202d}$, $X_{202e}$, $X_{202f}$, $X_{202g}$, $X_{202h}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{202}) = \mathbb{Q}(f_{202}), f_{78} = \frac{f_{202}^{2}  \frac{1}{2}}{f_{202}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2  8226x + 286474$, with conductor $126$  
Generic density of odd order reductions  $193/1792$ 