Julián Aguirre, Juan Carlos Peral
Published 2012-03-12Version 1
The elliptic curve y^2= x^3-Nx where N=m^4+n^4 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.
Sums of two biquadrates and elliptic curves of rank $\geq 4$
Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1
Trace of Frobenius endomorphism of an elliptic curve with complex multiplication
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