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

Jeon, Daeyeol; Kim, Chang; Lee, Yoonjin

doi:10.1090/S0025-5718-10-02369-0

Families of elliptic curves over cubic number fields with prescribed torsion subgroups
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by Daeyeol Jeon, Chang Heon Kim and Yoonjin Lee PDF

Math. Comp. 80 (2011), 579-591 Request permission

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.

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