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Counting points of small height on elliptic curves. (English) Zbl 0723.14026
Summary: Let k be a number field and let E be an elliptic curve defined over k. We prove a counting result which gives, among other things, the existence of a positive constant C, effectively computable in terms of k and E, with the following property: For any extension K of k of relative degree at most D (\(\geq 2)\), the absolute logarithmic canonical height of any non- torsion point of E(K) is at least \(CD^{-3}(\log (D))^{-2}\).

MSC:
14H52 Elliptic curves
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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