Central configurations in planar n-body problem with equal masses for n=5, 6, 7

We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for n = 5, 6, 7 with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For n = 8, 9, 10, we establish the existence of central configurations without any reflectional symmetry.