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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
이윤진scopus
Issue Date
2013
Journal Title
Journal of Number Theory
ISSN
0022-314XJCR Link
Citation
vol. 133, no. 1, pp. 115 - 122
Indexed
SCI; SCIE; SCOPUS WOS scopus
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
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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