FAMILIES OF ELLIPTIC CURVES OVER CUBIC NUMBER FIELDS WITH PRESCRIBED TORSION SUBGROUPS
- 주제(키워드) Elliptic curve , torsion , cubic number field , modular curve
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 AMER MATHEMATICAL SOC
- 발행년도 2011
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000098077
- 본문언어 영어
초록/요약
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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