Mathematical Theory and Applications ›› 2023, Vol. 43 ›› Issue (4): 48-58.doi: 10.3969/j.issn.1006-8074.2023.04.003

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The Mordell-Weil Groups of Cubic Pencils

Mo Jiali   

  1. Department of Mathematics, Soochow University, Suzhou 215006, China
  • Online:2023-12-28 Published:2024-01-03
  • Contact: Mo Jiali; E-mail: mojiali0722@126.com
  • Supported by:

    This work is supported by the Natural Science Foundation of Jiangsu Province(Nos. BK20181427, BK20211305) and Postgraduate

    Research & Practice Innovation Program of Jiangsu Province(No. KYCX22_3180

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Abstract: In this paper we study the influences of the base points of cubic pencils on the Mordell-Weil groups. Specifically, we investigate and classify the cubic pencils with 8, 7 and 6 base points in general position, and give some applications.

Key words: Base point, Cubic pencil, Elliptic curve, Mordell-Weil group

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