  We prove that there are only finitely many complex numbers $a$ and $b$ with
$4a^3+27b^2\not=0$ such that the three points $(1,*),(2,*),$ and $(3,*)$ are
simultaneously torsion on the elliptic curve defined in Weierstrass form by
$y^2=x^3+ax+b$. This gives an affirmative answer to a question raised by Masser
and Zannier. We thus confirm a special case in two dimensions of the relative
Manin-Mumford Conjecture formulated by Pink and Masser-Zannier.
