Curve name  $X_{92}$  
Index  $24$  
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} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{27}$  
Curves that $X_{92}$ minimally covers  $X_{27}$, $X_{36}$, $X_{43}$  
Curves that minimally cover $X_{92}$  $X_{195}$, $X_{205}$, $X_{207}$, $X_{259}$, $X_{278}$, $X_{305}$, $X_{306}$, $X_{371}$, $X_{92a}$, $X_{92b}$, $X_{92c}$, $X_{92d}$, $X_{92e}$, $X_{92f}$, $X_{92g}$, $X_{92h}$, $X_{92i}$, $X_{92j}$, $X_{92k}$  
Curves that minimally cover $X_{92}$ and have infinitely many rational points.  $X_{195}$, $X_{205}$, $X_{207}$, $X_{92a}$, $X_{92b}$, $X_{92c}$, $X_{92d}$, $X_{92e}$, $X_{92f}$, $X_{92g}$, $X_{92h}$, $X_{92i}$, $X_{92j}$, $X_{92k}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{92}) = \mathbb{Q}(f_{92}), f_{27} = \frac{f_{92}}{f_{92}^{2}  1}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2 + 33729345x  401153583974$, with conductor $6435$  
Generic density of odd order reductions  $19/168$ 