The symmetric central configurations of the 4-body problem with masses m1=m2≠m3=m4

We characterize the planar Central configurations of the 4-body problem with masses m1=m2≠m3=m4 which have an axis of symmetry.It is known that this problem has exactly two classes of convex Central configurations, one with the shape of a rhombus and the other with the shape of an isosceles trapezoid.We show that this 4-body problem also has exactly two classes of concave Central configurations with the shape of a kite, this proof is assisted by computer.