The general case over arbitrary number fields has been treated by Loïc Merel.  A good place to start would be Bas Edixhoven's Bourbaki exposé [*Rational torsion points on elliptic curves over number fields*][1], Séminaire Bourbaki, 36 (1993-1994), Exposé No. 782.

There is also an excellent set of notes by Joseph Œsterlé which were to be found on the [ICTP website][2].


  [1]: http://www.numdam.org/numdam-bin/fitem?id=SB_1993-1994__36__209_0
  [2]: http://www.ictp.it/