Curve name  $X_{117h}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{117}$  
Curves that $X_{117h}$ minimally covers  
Curves that minimally cover $X_{117h}$  
Curves that minimally cover $X_{117h}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 108t^{12} + 108t^{10} + 405t^{8}  432t^{6} + 108t^{2}  27\] \[B(t) = 432t^{18} + 648t^{16}  3564t^{14} + 4914t^{12} + 162t^{10}  3483t^{8} + 1512t^{6} + 324t^{4}  324t^{2} + 54\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3 + x^2  101887x + 12483848$, with conductor $25872$  
Generic density of odd order reductions  $193/1792$ 