On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II
type: Item
instance of: scholarly article
title: On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II
zbMATH Open document ID: 0877.11036
author: Shoichi Kihara
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-12-02T00:00:00Z
review text: By construction of the required number of independent points on the Mordell curve \[ y^2= x^3+k, \quad k\in\mathbb{Q}^* \] for certain \(k=k(t)\) depending on a parameter \(t\), the author shows that there are infinitely many non-isomorphic (over \(\mathbb{Q})\) Mordell curves of rank at least 7. This extends previous work of the author [\textit{S. Kihara}, Proc. Japan Acad., Ser. A 63, 76-78 (1987; Zbl 0629.14024)].
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 1022275
zbMATH Keywords: elliptic curve
zbMATH Keywords: Mordell curve
zbMATH Keywords: rank
reviewed by: Roelof J. Stroeker
MaRDI profile type: Publication
full work available at URL: pjaa.72.228
OpenAlex ID: W4234851232
cites work: Q3710637
cites work: On coprime integral solutions of \(y^ 2=x^ 3+k\)
cites work: On the rank of the elliptic curve \(y^ 2=x^ 3+k\)
DOI: 10.3792/PJAA.72.228
description: scientific article; zbMATH DE number 1022275