Reduced positive definite binary quadratic forms of discriminant minus thirty-nine ($h(-39)=4$)

The reduced positive definite binary quadratic form bounds $|b|\le a\le c$ and $b^2-4ac=-39$ imply $1\le a\le \sqrt{13}$. Enumerating $a=1,2,3$ and using the nonnegative boundary sign convention gives the four triples $(a,b,c)=(1,1,10),(2,1,5),(2,-1,5),(3,3,4)$. Thus the number of reduced forms is four.