Families of elliptic curves over cubic number fields with prescribed torsion subgroups. (English) Zbl 1214.11071
Summary: 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 [Acta Arith. 113, No. 3, 291–301 (2004; Zbl 1083.11038)]; 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.
MSC:
| 11G05 | Elliptic curves over global fields |
| 11G18 | Arithmetic aspects of modular and Shimura varieties |
Citations:
Zbl 1083.11038References:
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