Curve name  $X_{43}$  
Index  $12$  
Level  $8$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 5 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{11}$  
Curves that $X_{43}$ minimally covers  $X_{11}$  
Curves that minimally cover $X_{43}$  $X_{64}$, $X_{67}$, $X_{71}$, $X_{74}$, $X_{77}$, $X_{82}$, $X_{91}$, $X_{92}$, $X_{127}$, $X_{137}$, $X_{139}$, $X_{144}$  
Curves that minimally cover $X_{43}$ and have infinitely many rational points.  $X_{64}$, $X_{67}$, $X_{71}$, $X_{74}$, $X_{77}$, $X_{82}$, $X_{91}$, $X_{92}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{43}) = \mathbb{Q}(f_{43}), f_{11} = 2f_{43}^{2} + 8\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2 + 12x + 36$, with conductor $1176$  
Generic density of odd order reductions  $25/112$ 