Counting points of small height on elliptic curves. (English) Zbl 0723.14026

Masser, D. W.

Bull. Soc. Math. Fr. 117, No. 2, 247-265 (1989).

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

Keywords:

elliptic curve; absolute logarithmic canonical height; non-torsion point

References:

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