One half log discriminant
  We give a geometric proof that one may compute a particular generalized Mahler integral using equidistribution of preperiodic points of a dynamical system on the sphere. The dynamical system is associated to the multiplication by 2 map on an elliptic curve over a number field K with Weierstrass equation y^2 = P(x) (a Lattes dynamical system). 
Lucien Szpiro and Thomas J. Tucker