Curve name  $X_{237}$  
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} 7 & 14 \\ 2 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 4 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{83}$  
Curves that $X_{237}$ minimally covers  $X_{83}$, $X_{106}$, $X_{107}$  
Curves that minimally cover $X_{237}$  
Curves that minimally cover $X_{237}$ and have infinitely many rational points.  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{237}) = \mathbb{Q}(f_{237}), f_{83} = \frac{f_{237}}{f_{237}^{2} + 2}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  221950x + 40248384$, with conductor $147712$  
Generic density of odd order reductions  $45667/172032$ 