On the class numbers of the fields of the pn-torsion points of certain elliptic curves over Q

Fumio Sairaiji, Takuya Yamauchi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let E be an elliptic curve over Q with prime conductor p. For each positive integer n we put Kn:=Q(E[pn]). The aim of this paper is to estimate the order of the p-Sylow group of the ideal class group of Kn. We give a lower bound in terms of the Mordell-Weil rank of E(Q). As an application of our result, we give an example such that p2n divides the class number of the field Kn in the case of p=5077 for each positive integer n.

Original languageEnglish
Pages (from-to)277-289
Number of pages13
JournalJournal of Number Theory
Volume156
DOIs
Publication statusPublished - 2015 Nov 1

Keywords

  • Class number
  • Elliptic curve
  • Mordell-Weil rank

ASJC Scopus subject areas

  • Algebra and Number Theory

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