Sums of two biquadrates and elliptic curves of rank ≥ 4

2012/02/25 by Farzali Izadi, Izadi, F. A., Foad Khoshnam +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1202.5676

openalex publication_date 2012/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If an integer n is written as a sum of two biquadrates in two different ways, then the elliptic curve y²=x³-nx has rank ≥ 3. If moreover n is odd and the parity conjecture is true, then it has even rank ≥ 4. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained.

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