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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:[數學學系暨研究所] 期刊論文

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