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Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

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.

preprint2011arXivOpen access
Graeme Taylor
math.AGmath.NT
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Graeme Taylor

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