Estimating isogenies on elliptic curves
type: Item
instance of: scholarly article
title: Estimating isogenies on elliptic curves
zbMATH Open document ID: 0722.14027
DOI: 10.1007/BF01231178
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143776
review text: Let d be a positive integer, and let k be a number field of degree at most d. For an elliptic curve E defined by the Weierstrass equation \(y^ 2=4x^ 3-g_ 2x-g_ 3\) with \(g_ 2,g_ 3\in k\), put \(w(E)=\max (1,h(g_ 2),h(g_ 3))\), where h denotes the absolute logarithmic Weil height. Under these notations, the authors show that if \(E'\) is another elliptic curve defined over k isogenous to E, then there exists an isogeny between E and \(E'\) whose degree is at most \(c\cdot w(E)^ 4\), where c is a constant depending effectively on d. To give this estimation, the authors use the transcendence techniques which were used by \textit{D. K.} and \textit{G. V. Chudnovsky} [Proc. Natl. Acad. Sci. USA 82, 2212-2216 (1985; Zbl 0577.14034)].
Mathematics Subject Classification ID: 14K02
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 4189901
zbMATH Keywords: elliptic curve
zbMATH Keywords: logarithmic Weil height
zbMATH Keywords: isogeny
author: D. Masser
author: Gisbert Wüstholz
reviewed by: Tsutomu Sekiguchi
MaRDI profile type: Publication
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OpenAlex ID: W2061710893
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description: scientific article; zbMATH DE number 4189901