On Shioda-Inose structures of one-parameter families of K3 surfaces

JOURNAL OF NUMBER THEORY

卷:109

Article

Long, L

关键词: elliptic curve;    isogeny;    complex multiplication;    K3 surface;    Shioda-Inose structure;    Picard-Fuchs equation;    monodromy representation;   

DOI  :  10.1016/j.jnt.2004.06.009

来源: Elsevier

【 摘 要 】

We develop an algorithm to determine a one-parameter family of elliptic curves associated to a one-parameter family of K3 surfaces with generic Picard number 19 by a Shioda-Inose structure. The family of elliptic curves is determined up to an isomorphism and an isogeny. An application to a generalized congruence number problem is also discussed. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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