Curve name  $X_{83}$  
Index  $24$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{26}$  
Curves that $X_{83}$ minimally covers  $X_{22}$, $X_{26}$, $X_{29}$, $X_{39}$  
Curves that minimally cover $X_{83}$  $X_{232}$, $X_{237}$, $X_{275}$, $X_{276}$, $X_{370}$, $X_{402}$  
Curves that minimally cover $X_{83}$ and have infinitely many rational points.  $X_{232}$, $X_{237}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{83}) = \mathbb{Q}(f_{83}), f_{26} = \frac{f_{83}}{f_{83}^{2}  \frac{1}{8}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  2110x + 682176$, with conductor $202496$  
Generic density of odd order reductions  $1427/5376$ 