Sieving for rational points on hyperelliptic curves

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Siksek, Samir (2001)
  • Publisher: American Mathematical Society
  • Related identifiers: doi: 10.1090/S0025-5718-01-01275-3
  • Subject: QA
    arxiv: Mathematics::Algebraic Geometry | Mathematics::Number Theory | Nonlinear Sciences::Exactly Solvable and Integrable Systems

We give a new and efficient method of sieving for rational points\ud on hyperelliptic curves. This method is often successful in proving that a\ud given hyperelliptic curve, suspected to have no rational points, does in fact\ud have no rational points; we have often found this to be the case even when our\ud curve has points over all localizations Qp. We illustrate the practicality of the\ud method with some examples of hyperelliptic curves of genus 1.
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