On the equation Y2 = X5 + k

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number3
StatePublished - Jan 1 2008


  • Elliptic curve
  • Fifth powers
  • Genus two curve

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On the equation Y<sup>2</sup> = X<sup>5</sup> + k'. Together they form a unique fingerprint.

Cite this