Point counting on reductions of CM elliptic curves

Details Point counting on reductions of CM elliptic curves Point counting on reductions of CM elliptic curves

2007-06-25

arxiv.org/abs/0706.3711v4

Mathematics

Number Theory

Minor corrections. To appear in Journal of Number Theory

Scientific paper

10.1016/j.jnt.2009.01.020

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.

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