Kihara, Shoichi On the rank of the elliptic curves with a rational point of order 4. (English) Zbl 1050.11058 Proc. Japan Acad., Ser. A 80, No. 4, 26-27 (2004). 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 \(\geq 5\). Reviewer: Franz Lemmermeyer (Bilkent) Cited in 2 ReviewsCited in 3 Documents MSC: 11G05 Elliptic curves over global fields Keywords:elliptic curve; rank PDF BibTeX XML Cite \textit{S. Kihara}, Proc. Japan Acad., Ser. A 80, No. 4, 26--27 (2004; Zbl 1050.11058) Full Text: DOI OpenURL 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 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.