2018/05/31 by Pascal Autissier, Marc Hindry, Fabien Pazuki · 2 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Bounded function #Cryptography and Residue Arithmetic #Elliptic curve #Function (biology) #Property (philosophy) #Rank (graph theory) #Regulator #Schoof's algorithm #Supersingular elliptic curve #math.NT #msc:11G50 #msc:14G40
paper · pdf · doi:10.1093/imrn/rny285
published in International Mathematics Research Notices 2021(7), 4976-4993 (Oxford University Press)
openalex created_date 2018/05/17 · openalex publication_date 2018/12/10 · arxiv created 2019/02/27 · arxiv updated 2019/02/28 · openalex updated_date 2026/08/06
Abstract We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p>0. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.