2009/01/01 by Henri Cohen, Fabien Pazuki
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algorithm #Combinatorics #Computation #Computer science #Descent (aeronautics) #Elliptic curve #Geography #Geometric and Algebraic Topology #Interpretation (philosophy) #Isogeny #Mathematics #Pure mathematics #Rank (graph theory) #Supersingular elliptic curve #Torsion (gastropod) #math.NT #msc:11G05 #msc:14G05 #msc:14H52
paper · pdf · doi:10.4064/aa140-4-6
published as Acta Arithmetica 140.4, 2009, p. 369-404
openalex publication_date 2009/01/01 · arxiv created 2015/06/30 · arxiv updated 2015/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and we also give a geometric interpretation of these computations.