Curve name  $X_{97}$  
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 & 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  $X_{39}$  
Curves that $X_{97}$ minimally covers  $X_{39}$, $X_{45}$, $X_{47}$  
Curves that minimally cover $X_{97}$  $X_{254}$, $X_{260}$, $X_{264}$, $X_{275}$, $X_{301}$, $X_{303}$, $X_{304}$, $X_{308}$, $X_{309}$, $X_{310}$, $X_{311}$, $X_{312}$, $X_{377}$, $X_{380}$  
Curves that minimally cover $X_{97}$ and have infinitely many rational points.  $X_{304}$, $X_{308}$, $X_{309}$, $X_{312}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{97}) = \mathbb{Q}(f_{97}), f_{39} = \frac{4f_{97}^{2} + 1}{f_{97}^{2} + f_{97}  \frac{1}{4}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  558481500x  5079892400000$, with conductor $1159200$  
Generic density of odd order reductions  $1343/5376$ 