Curve name  $X_{91}$  
Index  $24$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 3 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 0 & 5 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{39}$  
Curves that $X_{91}$ minimally covers  $X_{39}$, $X_{43}$, $X_{50}$  
Curves that minimally cover $X_{91}$  $X_{256}$, $X_{259}$, $X_{261}$, $X_{276}$, $X_{286}$, $X_{287}$, $X_{288}$, $X_{289}$, $X_{290}$, $X_{291}$, $X_{300}$, $X_{352}$  
Curves that minimally cover $X_{91}$ and have infinitely many rational points.  $X_{288}$, $X_{289}$, $X_{291}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{91}) = \mathbb{Q}(f_{91}), f_{39} = \frac{f_{91}^{2} + 2}{f_{91}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy + y = x^3  8786x  296215$, with conductor $11109$  
Generic density of odd order reductions  $401/1792$ 