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On exact estimates of the torsion orders for points of curves of genus one. (Russian) Zbl 0638.14014
Let \(k\) be a number field of degree \(n\), \(F\) an elliptic curve over \(k\). Let \(p\) be an odd prime \(>3\) and assume that \(F(k)\) contains a point of order \(p^t\). The author claims that then \(p^{t-1}(p-1)\leq 6n\) and sketches the proof.

MSC:
14H25 Arithmetic ground fields for curves
14H52 Elliptic curves
14H45 Special algebraic curves and curves of low genus
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