Sums of two biquadrates and elliptic curves of rank $\geq 4$
  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. 
F. A. Izadi, F. Khoshnam, and K. Nabardi
math.NT