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Biquadrates and Elliptic Curves

Published 12 Mar 2012 in math.NT | (1203.2576v1)

Abstract: The elliptic curve y2= x3-Nx where N=m4+n4 has rank at least 2 over Q(m,n). When N can be written in two different ways as sum of two fourth powers, then we prove that the rank is at least 4.

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