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

Atsushi Sato

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the ramifications in the extensions of number fields arising from an isogeny of elliptic curves. In particular, we start with an elliptic curve with a rational torsion point, and show that the extension is unramified if and "only if" the point which generates the extension is reduced into a nonsingular point (we need to assume certain conditions in order to prove the "only if" part). We also study a characterization of quadratic number fields with class numbers divisible by 5.

Original languageEnglish
Pages (from-to)809-826
Number of pages18
JournalOsaka Journal of Mathematics
Volume48
Issue number3
Publication statusPublished - 2011 Sep 1

ASJC Scopus subject areas

  • Mathematics(all)

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