CM liftings of Supersingular Elliptic Curves

Details CM liftings of Supersingular Elliptic Curves CM liftings of Supersingular Elliptic Curves

2009-04-09

arxiv.org/abs/0904.1608v1

Journal de th\'eorie des nombres de Bordeaux, Vol. 21, no. 3, pp. 635-663, 2009

Mathematics

Number Theory

26 pages, 10 tables

Scientific paper

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|

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