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arXiv · 1111.2475

Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

Graeme Taylor
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Abstract

We give examples of points with particularly low height on elliptic curves over quadratic fields, recovered by a search over elliptic divisibility sequences. The smallest example identified satisfies dh(P)=0.0077127...: improving on the previous smallest for curves over quadratic fields of dh(P)=0.0194426... given by Everest and Ward; and comparable with some of the examples of smallest height on curves over Q tabulated by Elkies.

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Graeme Taylor. 2011-11-10. Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields. https://arxiv.org/abs/1111.2475

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