 

Clayton Petsche
Small rational points on elliptic curves over number fields


Published: 
September 2, 2006 
Keywords: 
Elliptic curves, heights, torsion points, Szpiro ratio, Lang's conjecture 
Subject: 
11G05, 11G07, 11G50 


Abstract
Let E/k be an elliptic curve over a number field. We obtain some quantitative refinements of results of HindrySilverman, giving an upper bound for the number of krational torsion points, and a lower bound for the canonical height of nontorsion krational points, in terms of expressions depending explicitly on the degree d=[k:Q] of k and the Szpiro ratio σ of E/k. The bounds exhibit only polynomial dependence on both d and σ.


Author information
Department of Mathematics, The University of Georgia, Athens, GA 306027403
clayton@math.uga.edu

