The selmer groups of elliptic curves and the ideal class groups of quadratic fields

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Title:	The selmer groups of elliptic curves and the ideal class groups of quadratic fields
Authors:	陳燕美;Chen, Yen-mei J.
Contributors:	淡江大學數學學系
Date:	1997-09-01
Issue Date:	2010-01-28
Publisher:	Taylor & Francis
Abstract:	Let D be an integer. Consider the elliptic curve E/Q :y2 = x3 + D, which has j-invariant 0. We can show that for this elliptic curve the rank of its 3-Selmer group is closely related to the 3-rank of the ideal class groups of the quadratic fields and . Fol the same family of curves Frey showed that, if D is a cube, the rank of the Selrner group of a 3-isogeny is related to the class number of the quadratic field [3]. Also Jan Nekevá[rbreve] proved some analogous result for elliptic curve given by Dy2 = 4x3 − 27 which is isomorphic to the curve given by y2 = x3 − 432D3 [4]. Our method is different from theirs and it can give a far more complete result for general D.
Relation:	Communications in Algebra 25(7), pp.2157-2167
DOI:	10.1080/00927879708825980
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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