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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 $\left|D\right|\>D_p$ implies that the map is necessarily surjective and then we compute explicitly the cases $\left|D\right|\<D_p$.