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Generators and integral points on twists of the Fermat cubic

Volume 168 / 2015

Yasutsugu Fujita, Tadahisa Nara Acta Arithmetica 168 (2015), 1-16 MSC: Primary 11G05, 11D59; Secondary 11G50. DOI: 10.4064/aa168-1-1


We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell–Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.


  • Yasutsugu FujitaCollege of Industrial Technology
    Nihon University
    2-11-1 Shin-ei
    Narashino, Chiba 275-8576, Japan
  • Tadahisa NaraFaculty of Engineering
    Tohoku-Gakuin University
    1-13-1 Chuo
    Tagajo, Miyagi 985-8537, Japan

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