Ramification of the Kummer extension generated from torsion points of elliptic curves

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Abstract

For a prime p, let p denote a fixed primitive pth root of unity. Let E be an elliptic curve over a number field k with a p-torsion point. Then the p-torsion subgroup of E gives a Kummer extension over k(p). In this paper, for p = 5 and 7, we study the ramification of such Kummer extensions using explicit Kummer generators directly computed by Verdure in 2006.

Original languageEnglish
Pages (from-to)1725-1734
Number of pages10
JournalInternational Journal of Number Theory
Volume11
Issue number6
DOIs
Publication statusPublished - Jan 1 2015
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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