Curve name  $X_{84c}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 3 & 3 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{84}$  
Curves that $X_{84c}$ minimally covers  
Curves that minimally cover $X_{84c}$  
Curves that minimally cover $X_{84c}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 27t^{12}  162t^{10} + 27t^{8} + 1188t^{6} + 1755t^{4} + 702t^{2}  27\] \[B(t) = 54t^{18} + 486t^{16} + 3564t^{14} + 15876t^{12} + 35640t^{10} + 37584t^{8} + 12852t^{6}  5508t^{4}  3726t^{2}  54\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  2008x + 295988$, with conductor $1200$  
Generic density of odd order reductions  $25/224$ 