Curve name  $X_{215}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{96}$  
Curves that $X_{215}$ minimally covers  $X_{96}$, $X_{119}$, $X_{120}$  
Curves that minimally cover $X_{215}$  $X_{469}$, $X_{470}$, $X_{483}$, $X_{485}$, $X_{215a}$, $X_{215b}$, $X_{215c}$, $X_{215d}$, $X_{215e}$, $X_{215f}$, $X_{215g}$, $X_{215h}$, $X_{215i}$, $X_{215j}$, $X_{215k}$, $X_{215l}$  
Curves that minimally cover $X_{215}$ and have infinitely many rational points.  $X_{215a}$, $X_{215b}$, $X_{215c}$, $X_{215d}$, $X_{215e}$, $X_{215f}$, $X_{215g}$, $X_{215h}$, $X_{215i}$, $X_{215j}$, $X_{215k}$, $X_{215l}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{215}) = \mathbb{Q}(f_{215}), f_{96} = \frac{2}{f_{215}^{2}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  246x  1485$, with conductor $735$  
Generic density of odd order reductions  $25/224$ 