An algorithm for the rank of elliptic curves
type: Item
instance of: scholarly article
title: An algorithm for the rank of elliptic curves
zbMATH Open document ID: 0807.14023
author: Chunlai Zhao
published in: Chinese Science Bulletin
publication date: 1995-03-08T00:00:00Z
review text: An asymptotic formula for the rank \(r\) of an elliptic curve \(E\) over the rationals \(\mathbb{Q}\) is given and a conjecture of \(S\). Lang on the size of the Néron-Tate height of basis points of the Mordell-Weil group \(E (\mathbb{Q})\) is claimed to lead to an algorithm for determining \(r\) provided Lang's conjecture is true and the constants involved can be effectively computed. No proofs are given. We mention that an algorithm for computing the rank \(r\) and a basis of the group \(E(\mathbb{Q})\), based on ideas of Manin and assuming the truth of the conjectures of Birch and Swinnerton-Dyer was developed by \textit{J. Gebel} and the reviewer [in Elliptic curves and related topics, CRM Proc. Lect. Notes 4, 61-83 (1994)].
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 468822
zbMATH Keywords: asymptotic rank of an elliptic curve
zbMATH Keywords: Néron-Tate height of basis points of the Mordell-Weil group
reviewed by: Horst G. Zimmer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 468822