Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D<0 such that the reduction map modulo a prime above p from elliptic curves with CM by 𝒪 D to supersingular elliptic curves in characteristic p is surjective. In the algorithm we first determine an explicit constant D p so that |D|>D p implies that the map is necessarily surjective and then we compute explicitly the cases |D|<D p .