On the Mordell--Weil group of the elliptic curve y^2=x^3+n

Yasutsugu Fujita; Tadahisa Nara

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arXiv · 1011.1077

On the Mordell--Weil group of the elliptic curve y^2=x^3+n

Yasutsugu Fujita·Tadahisa Nara

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Abstract

We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y^2=x^3+n, n \in Z) over Q with three explicit integral points. We show that the points are independent in certain cases. We describe how to compute bounds of the canonical heights of the points. Using the result we show that any pair in the three points can always be a part of a basis of the free part of the Mordell--Weil group.

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BibTeX RIS

Yasutsugu Fujita, Tadahisa Nara. 2010-11-04. On the Mordell--Weil group of the elliptic curve y^2=x^3+n. https://arxiv.org/abs/1011.1077

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