English

Point counting on reductions of CM elliptic curves

Number Theory 2009-08-06 v4

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

Keywords

Cite

@article{arxiv.0706.3711,
  title  = {Point counting on reductions of CM elliptic curves},
  author = {K. Rubin and A. Silverberg},
  journal= {arXiv preprint arXiv:0706.3711},
  year   = {2009}
}

Comments

Minor corrections. To appear in Journal of Number Theory