Families of elliptic curves over cubic number fields with prescribed torsion subgroups

Daeyeol Jeon, Chang Heon Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

In this paper we construct infinite families of elliptic curves with given torsion group structures over cubic number fields. This result provides explicit examples of the theoretical result recently developed by the first two authors and A. Schweizer; they determined all the group structures which occur infinitely often as the torsion of elliptic curves over cubic number fields. In fact, this paper presents an efficient way of constructing such families of elliptic curves with prescribed torsion group structures over cubic number fields.

Original languageEnglish
Pages (from-to)579-591
Number of pages13
JournalMathematics of Computation
Volume80
Issue number273
DOIs
StatePublished - 2010

Keywords

  • Cubic number field
  • Elliptic curve
  • Modular curve
  • Torsion

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