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arXiv · 1202.5676

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

F. A. Izadi·F. Khoshnam·K. Nabardi
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Abstract

If an integer $n$ is written as a sum of two biquadrates in two different ways, then the elliptic curve $y^2=x^3-nx$ has rank $\geq 3$. If moreover $n$ is odd and the parity conjecture is true, then it has even rank $\geq 4$. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained.

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F. A. Izadi, F. Khoshnam, K. Nabardi. 2012-02-25. Sums of two biquadrates and elliptic curves of rank $\geq 4$. https://arxiv.org/abs/1202.5676

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