Curve name  $X_{115c}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 2 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 9 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 4 & 5 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{115}$  
Curves that $X_{115c}$ minimally covers  
Curves that minimally cover $X_{115c}$  
Curves that minimally cover $X_{115c}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 1728t^{16}  7776t^{12}  5292t^{8}  1296t^{4}  108\] \[B(t) = 27648t^{24}  186624t^{20}  316224t^{16}  190512t^{12}  55080t^{8}  7776t^{4}  432\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  10700x  426000$, with conductor $1600$  
Generic density of odd order reductions  $419/2688$ 