Complex Multiplication Tests for Elliptic Curves

2004/09/26 by Denis Charles, Charles, Denis
Mathematics · #11G05 #11G15 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G05 #msc:11G15

paper · pdf · doi:10.48550/arxiv.math/0409501

13 pages, 2 tables, 1 appendix

arxiv created 2004/09/26 · arxiv updated 2009/12/01

Abstract

We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can be adapted to yield the discriminant of the endomorphism ring of the curve.

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