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    Title      l  Families of elliptic curves over quartic number fields with prescribed torsion subgroups
    Author   l  Daeyeol Jeon, Chang Heon Kim and Yoonjin Lee
    Date   l  2009-10-05
    Category   l  ASARC-Preprint-09-34
    Download    l 1254724369_0.931286.pdf  
We construct infinite families of elliptic curves with given torsion group struc-
tures over quartic number fields. Recently the first two authors and Park determined
all 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.