Curve name  $X_{14}$  
Index  $6$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 0 \\ 2 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 7 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  Elliptic curves with discriminant $\Delta$ whose $2$isogenous curve has discriminant in the square class of $2\Delta$  
Chosen covering  $X_{6}$  
Curves that $X_{14}$ minimally covers  $X_{6}$  
Curves that minimally cover $X_{14}$  $X_{38}$, $X_{44}$  
Curves that minimally cover $X_{14}$ and have infinitely many rational points.  $X_{38}$, $X_{44}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{14}) = \mathbb{Q}(f_{14}), f_{6} = 2f_{14}^{2}  16\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  9x  10$, with conductor $1152$  
Generic density of odd order reductions  $5123/21504$ 