Infinite families of elliptic curves over Dihedral quartic number fields
- Title
- Infinite families of elliptic curves over Dihedral quartic number fields
- Author
- 김창헌
- Keywords
- Elliptic curve; Torsion; Dihedral quartic number field; Modular curve
- Issue Date
- 2013-01
- Publisher
- Elsevier Science B.V. Amsterdam
- Citation
- Journal of Number Theory, January 2013, 133(1), p.115-122
- Abstract
- 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 Et in the constructed families, the Galois group Gal(L/Q) is isomorphic to the Dihedral group D4 of order 8 for the Galois closure L of K over Q, where K is the defining field of (Et,Qt) and Qt is a point of Et of order N. We also notice that the plane model for the modular curve X1(24) found in Jeon et al. (2011) [1] is in the optimal form, which was the missing case in Sutherlandʼs work (Sutherland, 2012 [12]).
- URI
- https://www.sciencedirect.com/science/article/pii/S0022314X12002119https://repository.hanyang.ac.kr/handle/20.500.11754/69809
- ISSN
- 0022-314X
- DOI
- 10.1016/j.jnt.2012.06.014
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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