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

Jeon, Daeyeol; Kim, Chang Heon; Lee, Yoonjin

doi:10.1090/S0025-5718-2011-02493-2

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

Math. Comp. 80 (2011), 2395-2410 Request permission

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.

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