Integral points on elliptic curves and 3-torsion in class groups

HA Helfgott, A Venkatesh

Research output: Contribution to journalArticle (Academic Journal)peer-review

34 Citations (Scopus)

Abstract

We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and methods based on quasiorthogonality in the Mordell-Weil lattice ([Sil6], [GS], [He]). We apply our results to break previous bounds on the number of elliptic curves of given conductor and the size of the 3-torsion part of the class group of a quadratic field. The same ideas can be used to count rational points on curves of higher genus.
Translated title of the contributionIntegral points on elliptic curves and 3-torsion in class groups
Original languageEnglish
Pages (from-to)527 - 550
Number of pages24
JournalJournal of the American Mathematical Society
Volume19 (3)
DOIs
Publication statusPublished - Jul 2006

Bibliographical note

Publisher: American Mathematical Society
Other identifier: IDS number 042FR

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