Complex Multiplication Tests for Elliptic Curves

Details Complex Multiplication Tests for Elliptic Curves Complex Multiplication Tests for Elliptic Curves

2004-09-26

arxiv.org/abs/math/0409501v1

Mathematics

Number Theory

13 pages, 2 tables, 1 appendix

Scientific paper

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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