Curve name  $X_{210}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 1 & 2 \\ 14 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 10 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 14 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{61}$  
Curves that $X_{210}$ minimally covers  $X_{61}$, $X_{111}$, $X_{112}$  
Curves that minimally cover $X_{210}$  $X_{210a}$, $X_{210b}$, $X_{210c}$, $X_{210d}$  
Curves that minimally cover $X_{210}$ and have infinitely many rational points.  $X_{210a}$, $X_{210b}$, $X_{210c}$, $X_{210d}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{210}) = \mathbb{Q}(f_{210}), f_{61} = \frac{2}{f_{210}^{2}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2  51x + 152$, with conductor $153$  
Generic density of odd order reductions  $9249/57344$ 