Lattices and Rational Points
Copyright policy )Lattices and Rational Points
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.
- University of Göttingen Germany
- ETH Zurich Switzerland
curves, Heights; Rational points; Curves; Elliptic curves, Heights, heights, rational points, heights; rational points; curves; elliptic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, QA1-939, elliptic curves, Elliptic curves, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Mathematics, Curves
curves, Heights; Rational points; Curves; Elliptic curves, Heights, heights, rational points, heights; rational points; curves; elliptic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, QA1-939, elliptic curves, Elliptic curves, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Mathematics, Curves
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