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

Daeyeol Jeon, Chang Heon Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We construct infinite families of elliptic curves with given torsion group structures over quartic number fields. In a 2006 paper, the first two authors and Park determined all of the group structures which occur infinitely often as the torsion of elliptic curves over quartic number fields. Our result presents explicit examples of their theoretical result. This paper also presents an efficient way of finding such families of elliptic curves with prescribed torsion group structures over quadratic or quartic number fields

Original languageEnglish
Pages (from-to)2395-2410
Number of pages16
JournalMathematics of Computation
Volume80
Issue number276
DOIs
StatePublished - 2011

Keywords

  • Elliptic curve
  • Modular curve
  • Quadratic number field
  • Quartic number field
  • Torsion

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