Some quartic curves with no points in any cubic field

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Abstract

A sufficient condition is given such that the curves ΓD: x4 + y4 = Dz4 have no points in any odd-degree (greater than 1) extension field of the rationals. The condition is in terms of the rational rank of an elliptic curve in the Jacobian of ΓD. Various examples are given.

Original languageEnglish (US)
Pages (from-to)193-214
Number of pages22
JournalProceedings of the London Mathematical Society
Volumes3-52
Issue number2
DOIs
StatePublished - 1986

ASJC Scopus subject areas

  • Mathematics(all)

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