  We apply the theory of Bruhat-Tits trees to the study of optimal embeddings
of two and three dimensional commutative orders into quaternion algebras.
Specifically, we determine how many conjugacy classes of global Eichler orders
in a quaternion algebra yield optimal representations of such orders. This
completes the previous work by C. Maclachlan, who considered only Eichler
orders of square free level and integral domains as sub-orders. The same
technique is used in the second part of this work to compute local embedding
numbers, extending previous results by J. Brzezinski.
