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arXiv · 0706.3711

Point counting on reductions of CM elliptic curves

K. Rubin·A. Silverberg
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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.

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K. Rubin, A. Silverberg. 2009-08-06. Point counting on reductions of CM elliptic curves. https://doi.org/10.1016/j.jnt.2009.01.020

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