I'm looking for an explanation of the following result:

If D is a maximal order in a definite (i.e. ramified at infinity) quaternion algebra B over $\mathbb{Q}$, and $\phi : B\otimes\mathbb{R}\rightarrow\mathbb{H}$ is an isomorphism over $\mathbb{R}$ (where $\mathbb{H}$ is the Hamiltonian quaternions over $\mathbb{R}$), then the co-volume of $\phi(D)$ in $\mathbb{H}$ (with respect to the Lebesgue measure for the basis 1,i,j,k) is $(1/4) \cdot Disc(D)$ (where the discriminant is the determinant of the trace form on a basis of $D$, or, equivalently since $D$ is maximal, the product of the finite primes where $B$ ramifies).

Right now the only way I have to see this is through an explicit calculation using the generators for maximal orders described in a paper by Ibukiyama available here: Link , but I feel like there must be a nice way to see this using just properties of maximal orders without having to calculate with an explicit basis. Any ideas or references?