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Lattices and Rational Points

Author

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  • Evelina Viada

    (Mathematisches Institut, Georg-August-Universität, Bunsenstraße 3–5, D-D-37073 Göttingen, Germany)

Abstract

In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex Multiplication (CM). We then apply our result to give a method for finding the rational points on such curves, when E has Q -rank ≤ N - 1 . We also give some explicit examples. This result generalises from rank 1 to rank N - 1 previous results of S. Checcoli, F. Veneziano and the author.

Suggested Citation

  • Evelina Viada, 2017. "Lattices and Rational Points," Mathematics, MDPI, vol. 5(3), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:3:p:36-:d:104149
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