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자연과학대학
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Infinite families of elliptic curves over Dihedral quartic number fields
Title
Infinite families of elliptic curves over Dihedral quartic number fields
Authors
Jeon D.
;
Kim C.H.
;
Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진
Issue Date
2013
Journal Title
Journal of Number Theory
ISSN
0022-314X
Citation
Journal of Number Theory vol. 133, no. 1, pp. 115 - 122
Indexed
SCI; SCIE; SCOPUS
Document Type
Article
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 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.
DOI
10.1016/j.jnt.2012.06.014
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