Torsion points on elliptic curves in Weierstrass form

We prove that there are only finitely many complex numbers a and b with 4a3+27b2≠0 such that the three points (1,∗),(2,∗), and (3,∗) are simultaneously torsion on the elliptic curve defined in Weierstrass form by y2=x3+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.