The Legendre family of elliptic curves has the remarkable property that both its periods and its supersingular locus have descriptions in terms of the hypergeometric function [math] . In this work we study elliptic curves and elliptic integrals with respect to the hypergeometric functions [math] and [math] , and prove that the supersingular [math] -invariant locus of certain families of elliptic curves are given by these functions.