In the literature there are several different definitions of what is often referred to as Beilinson's height pairing (see for example section 4.3.8 of Gillet and Soulé's paper [Arithmetic intersection theory][1], and this [note][2] of Müller-Stach). The height pairing is supposed to generalize the [Neron-Tate height pairing][3]. Is there a precise statement in the literature where Beilinson's height pairing for an elliptic curve over $\mathbb{Q}$ is compared to the Neron-Tate pairing? 


  [1]: http://www.numdam.org/numdam-bin/fitem?id=PMIHES_1990__72__93_0
  [2]: http://hodge.mathematik.uni-mainz.de/~stefan/papers/cime.pdf
  [3]: http://en.wikipedia.org/wiki/Neron%25E2%2580%2593Tate_height