Ternary quadratic forms over number fields with small class number (Q898821)

The authors use the correspondence of ternary quadratic forms over number fields with quaternion orders for the enumeration of all positive definite ternary quadratic forms with class number 1 or 2 over totally real number fields. The method is to enumerate all definite quaternion orders of type number 1 or 2 over totally real number fields using Eichler's mass formula. Furthermore, all definite quaternion orders of ideal class number 1 or 2 are listed.