Infinite families of elliptic curves over Dihedral quartic number fields
- 주제(키워드) Dihedral quartic number field , Elliptic curve , Modular curve , Torsion
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press
- 발행년도 2013
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000094258
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jnt.2012.06.014
초록/요약
We find infinite families of elliptic curves over quartic number fields with torsion group Z/NZ with N = 20, 24. We prove that for each elliptic curve E t in the constructed families, the Galois group Gal(L/Q) is isomorphic to the Dihedral group D 4 of order 8 for the Galois closure L of K over Q, where K is the defining field of (E t, Q t) and Q t is a point of E t of order N. We also notice that the plane model for the modular curve X 1(24) found in Jeon et al. (2011) [1] is in the optimal form, which was the missing case in Sutherland's work (Sutherland, 2012 [12]). © 2012 Elsevier Inc.
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