Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

Details Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

2011-11-10

arxiv.org/abs/1111.2475v1

Mathematics

Number Theory

Scientific paper

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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