= Class number one for discriminant minus sixty-seven
{title2=$D=-67$}
For negative discriminant $-67$, a <reduced positive definite binary quadratic form> satisfies $1\le a\le\sqrt{67/3}<5$ and $b$ odd with $|b|\le a$. Checking $4a\mid b^2+67$ leaves only $(a,b,c)=(1,1,17)$ under the boundary convention. The <reduction algorithm for a positive definite binary quadratic form> therefore puts every form in this one <proper equivalence of binary quadratic forms> class. Its unimodular shears give infinitely many distinct forms $x^2+(2n+1)xy+(n^2+n+17)y^2$.
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