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Point counting on reductions of CM elliptic curves

2007/06/30 by K. Rubin, A. Silverberg · 1 citation
Mathematics · #math.NT #msc:11G05 #msc:11G15 #msc:11G20

paper · pdf · doi:10.1016/j.jnt.2009.01.020

Minor corrections. To appear in Journal of Number Theory

arxiv created 2009/08/06 · arxiv updated 2009/12/01

Abstract

We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM Q-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.

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