Linearly Normal Curves in P^n

Pasarescu, Ovidiu

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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 $| D | > D_{p}$ implies that the map is necessarily surjective and then we compute explicitly the cases $| D | < D_{p}$ .