On the class numbers of certain number fields obtained from points on elliptic curves II

Atsushi Sato

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We construct a family of cyclic extensions of number fields, in which every finite place is unramified, from an elliptic curve with a rational torsion point. As an application, we obtain such polynomials F(X) of rational coefficients that have the following property: For a rational number ξ chosen at random, the class number of the field generated by the square root of F(ξ) is "often" divisible by 3, 5 or by 7.

Original languageEnglish
Pages (from-to)375-390
Number of pages16
JournalOsaka Journal of Mathematics
Volume45
Issue number2
Publication statusPublished - 2008 Jun 1

ASJC Scopus subject areas

  • Mathematics(all)

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