Sums of two biquadrates and elliptic curves of rank $\geq 4$

Details Sums of two biquadrates and elliptic curves of rank $\geq 4$ Sums of two biquadrates and elliptic curves of rank $\geq 4$

2012-02-25

arxiv.org/abs/1202.5676v4

Mathematics

Number Theory

7 pages, 2 tables

Scientific paper

Let $n$ be an odd positive integer which can be written in two different ways
as sums of two biquadrates. Then we show that the elliptic curve $y^2=x^3-nx$
has even rank$\geq 4$. If $n$ is even number with the same property, then the
curve has odd rank$\geq 3$. Moreover, some examples of ranks equal to 4, 5, 6,
7, 8 and 10, are also given.

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