On exact estimates of the torsion orders for points of curves of genus one. (Russian) Zbl 0638.14014

Dem’yanenko, V. A.

Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 151, 57-65 (1986).

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.

Reviewer: Yu. G. Zarhin (Moskva)

MSC:

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

Keywords:

torsion of elliptic curves