On the equation Y2 = X5 + k

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2 Scopus citations

Abstract

We show that there are infinitely many nonisomorphic curves Y2 = X5 + k, k ∈ ℤ, possessing at least twelve finite points for k > 0, and at least six finite points for k < 0. We also determine all rational points on the curve Y2 = X5 − 7.

Original languageEnglish (US)
Pages (from-to)371-374
Number of pages4
JournalExperimental Mathematics
Volume17
Issue number3
DOIs
StatePublished - Jan 1 2008

Keywords

  • Elliptic curve
  • Fifth powers
  • Genus two curve

ASJC Scopus subject areas

  • Mathematics(all)

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