If an integer n is written as a sum of two biquadrates in two different
ways, then the elliptic curve y2=x3βnx has rank β₯3. If moreover n
is odd and the parity conjecture is true, then it has even rank β₯4.
Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also
obtained.Comment: 11 pages, 2 table