On the rank of the elliptic curves with a rational point of order 4. II. (English) Zbl 1073.11038

In this note the author constructs an elliptic curve defined over \(\mathbb Q(t)\) with nonconstant \(j\)-invariant, a rational point of order \(4\), and Mordell-Weil rank \(\geq 5\).
Part I, cf. ibid. 80, No. 4, 26–27 (2004; Zbl 1050.11058).


11G05 Elliptic curves over global fields
14G25 Global ground fields in algebraic geometry


Zbl 1050.11058
Full Text: DOI


[1] Kihara, S.: On the rank of elliptic curves with a rational points of order 4. Proc. Japan Acad. 80A ., 26-27 (2004). · Zbl 1050.11058 · doi:10.3792/pjaa.80.26
[2] Kihara, S.: On the rank of elliptic curves with three rational points of order 2. III. Proc. Japan Acad. 80A ., 13-14 (2004). · Zbl 1050.11059 · doi:10.3792/pjaa.80.13
[3] Silverman, J. H.: The Arithmetic of Elliptic Curves. Grad. Texts in Math., 106. Springer, New York (1986). · Zbl 0585.14026
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