2016/05/11 by Clemens Heuberger, Michela Mazzoli
Computer Science · Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics #Discrete mathematics #Elliptic curve #Field (mathematics) #Finite field #Historical and Political Studies #Mathematics #Pure mathematics #math.NT #msc:11A05 #msc:11G20
paper · pdf · doi:10.1016/j.jnt.2017.05.028
published as J. Number Theory 181 (2017), 89-98
arxiv created 2016/05/11 · openalex created_date 2016/06/24 · openalex publication_date 2017/08/04 · arxiv updated 2017/08/30 · openalex updated_date 2026/08/06
Consider a pair of ordinary elliptic curves E and E′ defined over the same finite field Fq. Suppose they have the same number of Fq-rational points, i.e. |E(Fq)|=|E′(Fq)|. In this paper we characterise for which finite field extensions Fqk, k≥1 (if any) the corresponding groups of Fqk-rational points are isomorphic, i.e. E(Fqk)≅E′(Fqk).