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arXiv · 0904.1608

CM liftings of Supersingular Elliptic Curves

Ben Kane
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Abstract

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 $\order_{D}$ to supersingular elliptic curves in characteristic $p$. 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 $|D|<D_p$.

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Ben Kane. 2009-04-09. CM liftings of Supersingular Elliptic Curves. https://arxiv.org/abs/0904.1608

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