A lower bound for the canonical height on elliptic curves over abelian extensions

2003/05/01 by Joseph H. Silverman
Mathematics · #math.NT #math.AC #msc:11G05 #msc:11G10 #msc:14G25 #msc:14K15

paper · pdf

published as Journal of Number Theory 104 (2004), 353--372

arxiv created 2003/05/01 · arxiv updated 2009/11/30

Abstract

Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prove that there is a positive constant C(E/K) so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K).

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