Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 arXiv:
 arXiv:1111.2475
 Bibcode:
 2011arXiv1111.2475T
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 14H52