Curve name  $X_{232}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 11 & 11 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 10 \\ 2 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{83}$  
Curves that $X_{232}$ minimally covers  $X_{83}$, $X_{105}$, $X_{124}$  
Curves that minimally cover $X_{232}$  
Curves that minimally cover $X_{232}$ and have infinitely many rational points.  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{232}) = \mathbb{Q}(f_{232}), f_{83} = \frac{\frac{1}{4}f_{232}^{2} + f_{232}  1}{f_{232}^{2} + 4}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  760x + 8448$, with conductor $4352$  
Generic density of odd order reductions  $45667/172032$ 