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

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

2003-05-01

arxiv.org/abs/math/0305041v1

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

Mathematics

Number Theory

Scientific paper

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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