Point counting on reductions of CM elliptic curves

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 $\mathbf{Q}$-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.

Minor corrections. To appear in Journal of Number Theory

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• Distribution of root numbers of Hecke characters attached to some elliptic curves
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