  The asymptotic behaviour of the Neron-Tate height of Heegner points on a
rational elliptic curve attached to an arithmetically normalized new cusp form
f of weight 2, level N and trivial character is studied in this paper. By
Gross-Zagier formula, this height is related to the special value at the
critical point for the derivative of the Rankin-Selberg convolution of f with a
certain weight one theta series attached to some ideal class of some imaginary
quadratic field. Asymptotic formula for the first moments asociated to these
Dirichlet series are proved and experimental results are carefully discussed.
