  Let $A$ be a definite quaternion algebra over $\mathbb Q$, with discriminant
$D_A$, and $O$ a maximal order of $A$. We show that the minimum of the positive
definite hamiltonian binary forms over $O$ with discrimiminant $-1$ is
$\sqrt{D_A}$. When the different of $O$ is principal, we provide an explicit
form representing this minimum, and when $O$ is principal, we give the list of
the equivalence classes of all such forms. We also give criteria and algorithms
to determine when the different of $O$ is principal.
