Two distinguished classes of discriminant minus eight q ($D=-8q$)

For an odd prime number $q$, the primitive positive definite formshave discriminant $-8q$ and lie in distinct proper equivalence classes. The first represents one, whereas the second has minimum positive value two.

If $q\equiv 3(\mathrm{mod}8)$ is prime and $h(-8q)=2$, then for every prime $p>q$,for some integers $x,y$ exactly when $p\equiv \pm 1(\mathrm{mod}8)$ and $p$ is a quadratic residue modulo $q$.