Computations of the rank of elliptic curve \(y^ 2=x^ 3-n^ 2x\)
type: Item
instance of: scholarly article
title: Computations of the rank of elliptic curve \(y^ 2=x^ 3-n^ 2x\)
zbMATH Open document ID: 0820.14040
author: Hideo Wada
author: Mayako Tairo
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-12-19T00:00:00Z
review text: In this paper the rank of the elliptic curve \(y^ 2 = x^ 3 - n^ 2x\) \((n\) is a square free integer) for \(n < 1000\), and the order of the Hasse-Weil function, for \(n < 30000\), are computed. For this purpose, the authors utilize programs written in UBASIC that apply the methods given by \textit{J. S. Chahal} in ``Topics in number theory'' [Univ. Ser. Math. (New York 1988; Zbl 0711.11001)], and by \textit{J. E. Cremona} in ``Algorithms for modular elliptic curves'' (Cambridge 1992; Zbl 0758.14042).
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 11D25
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 701472
zbMATH Keywords: rank of elliptic curve
zbMATH Keywords: order of the Hasse-Weil function
reviewed by: J. Rafael Sendra
describes a project that uses: UBASIC
describes a project that uses: ecdata
MaRDI profile type: Publication
full work available at URL: pjaa.70.154
OpenAlex ID: W2046073982
cites work: Notes on elliptic curves. II.
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cites work: Q4003857
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cites work: All congruent numbers less than 10 000
cites work: Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
DOI: 10.3792/PJAA.70.154
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description: scientific article; zbMATH DE number 701472