|
Let E be an elliptic curve over Q of analytic rank 2, and let
K be a quadratic imaginary field such that each prime dividing the
conductor of E splits in K. We use Heegner points to define
GF(ell)-rational points in E(GF(ell))/p for
certain inert primes ell, p of K. We then give the first
complete algorithm for computing these points z, and find that
they are frequently nonzero, which provides the first ever proof of
a deep conjecture of Kolyvagin in these cases. We also observe that
if any z is nonzero then E(Q) has algebraic rank at most 2.
|