Families of elliptic curves over quartic number fields with prescribed torsion subgroups
- 주제(키워드) Elliptic curve , Modular curve , Quadratic number field , Quartic number field , Torsion
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 American Mathematical Society
- 발행년도 2011
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000092715
- 본문언어 영어
- Published As http://dx.doi.org/10.1090/S0025-5718-2011-02493-2
초록/요약
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 © 2011 American Mathematical Society.
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