On the rank of elliptic curves with a rational point of order 3. (English) Zbl 0959.11024

In this paper the author constructs an elliptic curve over \(\mathbb Q(t)\) of rank at least 6 with a rational point of order 3.


11G05 Elliptic curves over global fields
14H52 Elliptic curves
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[1] Campbell, G.: Finding elliptic curves and infinite families of elliptic curves defined over \(\mathbf{Q}\) of large rank (1999) (Ph. D. Thesis, Rutgers University).
[2] Silverman, J. H.: The arithmetic of elliptic curves. Grad. Texts in Math., vol. 106, Springer, New York (1986). · Zbl 0585.14026
[3] Top, J.: Descent by 3-isogeny and 3-rank of quadratic fields. Advances in Number Theory. Oxford Science Publications, Oxford Univ. Press, Oxford, pp. 303-317 (1993). · Zbl 0804.11040
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