On the rank of elliptic curves with three rational points of order 2. II
type: Item
instance of: scholarly article
title: On the rank of elliptic curves with three rational points of order 2. II
zbMATH Open document ID: 0906.11025
author: Shoichi Kihara
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-02-07T00:00:00Z
review text: The author improves the result of Part I [\textit{S. Kihara} Proc. Japan Acad., Ser. A 73, No. 5, 77-78 (1997; Zbl 0906.11024)]. He proves that there exist infinitely many elliptic curves defined over \(\mathbb{Q}\) with rank \(\geq 5\) with the \(2\)-division subgroup \(\mathbb{Q}\)-rational. The construction is explicit.
reviewed by: Federico Pellarin
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 1160940
zbMATH Keywords: elliptic curves over global fields
zbMATH Keywords: Mordell-Weil group
zbMATH Keywords: \(\mathbb{Q}\)-rational 2-division subgroup
MaRDI profile type: Publication
full work available at URL: pjaa.73.151
OpenAlex ID: W2027337441
cites work: Q3710637
cites work: On the rank of elliptic curves with three rational points of order 2
cites work: On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II
DOI: 10.3792/PJAA.73.151
description: scientific article; zbMATH DE number 1160940