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  • 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 $(1/4) \cdot Disc(D)$
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