Curve name  $X_{115a}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 3 & 3 \\ 4 & 1 \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 $X_{115a}$ minimally covers  
Curves that minimally cover $X_{115a}$  
Curves that minimally cover $X_{115a}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 432t^{16}  1944t^{12}  1323t^{8}  324t^{4}  27\] \[B(t) = 3456t^{24} + 23328t^{20} + 39528t^{16} + 23814t^{12} + 6885t^{8} + 972t^{4} + 54\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  50x + 125$, with conductor $200$  
Generic density of odd order reductions  $103/672$ 