On the class numbers of the fields of the p n -torsion points of elliptic curves over Q

Fumio Sairaiji, Takuya Yamauchi

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1 Citation (Scopus)

Abstract

Let E be an elliptic curve over Q which has multiplicative reduction at a fixed prime p. Assume E has multiplicative reduction or potentially good reduction at any prime not equal to p. For each positive integer n we put K n := Q(E[p n ]). The aim of this paper is to extend the authors’ previous results in [13] concerning with the order of the p-Sylow group of the ideal class group of K n to more general setting. We also modify the previous lower bound of the order given in terms of the Mordell–Weil rank of E(Q) and the ramification related to E.

Original languageEnglish
Pages (from-to)893-915
Number of pages23
JournalJournal de Theorie des Nombres de Bordeaux
Volume30
Issue number3
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Class number
  • Elliptic curves
  • Mordell-Weil rank

ASJC Scopus subject areas

  • Algebra and Number Theory

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