Curve name  $X_{40a}$  
Index  $24$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  No  
Generating matrices  $ \left[ \begin{matrix} 1 & 1 \\ 6 & 11 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 14 & 15 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 2 & 1 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{40}$  
Curves that $X_{40a}$ minimally covers  
Curves that minimally cover $X_{40a}$  
Curves that minimally cover $X_{40a}$ and have infinitely many rational points.  
Model  $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = 17280t^{4}  6912t^{3}  864t^{2}  864t  270\] \[B(t) = 774144t^{6}  165888t^{5} + 373248t^{4} + 235008t^{3} + 46656t^{2}  2592t  1512\]  
Info about rational points  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 = x^3  x^2  525x  4459$, with conductor $1792$  
Generic density of odd order reductions  $106595/344064$ 