Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
Number Theory
2011-11-11 v1 Algebraic Geometry
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.
Cite
@article{arxiv.1111.2475,
title = {Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields},
author = {Graeme Taylor},
journal= {arXiv preprint arXiv:1111.2475},
year = {2011}
}