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On the rank of the elliptic curves with a rational point of order 4. (English) Zbl 1050.11058
The author proves the following two theorems: 1) There is an elliptic curve defined over \(\mathbb Q(t)\) with a rational point of order \(4\) and rank \(\geq 4\). 2) There are infinitely many elliptic curves defined over \(\mathbb Q\) with a rational point of order \(4\) and rank \(\geq 5\).

MSC:
11G05 Elliptic curves over global fields
Keywords:
elliptic curve; rank
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References:
[1] Kihara, S.: On the rank of the elliptic curve \(y^2=x^3+kx\). Proc. Japan Acad., 74A , 115-116 (1998). · Zbl 0919.11039 · doi:10.3792/pjaa.74.115
[2] Mestre, J.-F.: Rang de courbes elliptiques d’invariant donné. C. R. Acad. Sci. Paris Sér. I Math., 314 , 919-922 (1992). · Zbl 0766.14023
[3] Nagao, K.: On the rank of elliptic curve \(y^2=x^3-kx\). Kobe J. Math., 11 , 205-210 (1994). · Zbl 0855.11026
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