A covariant functor on the elliptic curves with complex multiplication is
constructed. The functor takes values in the noncommutative tori with real
multiplication. A conjecture on the rank of an elliptic curve is formulated.Comment: 13 pages, 2 figures; to appear Osaka J. Mathematics 46 (2009), No.2;
http://projecteuclid.org/euclid.ojm/124541568
