 Reduced positive definite binary quadratic forms of discriminant minus thirty-nine (source code)

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= Reduced positive definite binary quadratic forms of discriminant minus thirty-nine
{title2=$h(-39)=4$}

The <reduced positive definite binary quadratic form> bounds $|b|\leq a\leq c$ and $b^2-4ac=-39$ imply $1\leq a\leq\sqrt{13}$. 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.

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