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

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

2010-11-04

arxiv.org/abs/1011.1077v1

Mathematics

Number Theory

25 pages

Scientific paper

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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