Over Q, the definite quaternion algebras with a unique conjugacy class of maximal orders, i.e. "with class number one", are those with discriminant 2,3,5,7, and 13.
What is a reference for this result?
What are some examples of definite quaternions of class number one, over other totally real fields?
For a fixed real quadratic field, is there a known classification of definite quaternion algebras class number one?