Curve name  $X_{74}$  
Index  $24$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 2 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{26}$  
Curves that $X_{74}$ minimally covers  $X_{26}$, $X_{43}$, $X_{47}$  
Curves that minimally cover $X_{74}$  $X_{275}$, $X_{278}$  
Curves that minimally cover $X_{74}$ and have infinitely many rational points.  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{74}) = \mathbb{Q}(f_{74}), f_{26} = \frac{f_{74}}{f_{74}^{2}  \frac{1}{4}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2 + 572906x  1075433592$, with conductor $16810$  
Generic density of odd order reductions  $109/448$ 