Curve name  $X_{117c}$  
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} 3 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 8 & 5 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{117}$  
Curves that $X_{117c}$ minimally covers  
Curves that minimally cover $X_{117c}$  
Curves that minimally cover $X_{117c}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 108t^{8} + 432t^{4}  108\] \[B(t) = 432t^{12} + 3240t^{8}  2592t^{4} + 432\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  8317x + 294733$, with conductor $14784$  
Generic density of odd order reductions  $307/2688$ 