Lattice calculation of alpha(s) in momentum scheme

We compute the flavorless running coupling constant of QCD from the three g luon vertex in the (regularisation independent) momentum subtraction renorm alisation scheme. This is performed on the lattice with high statistics. Th e expected color dependence of the Green functions is verified. There are s ignificant O(a(2)mu(2)) effects which can be consistently controlled. Scali ng is demonstrated when the renormalisation scale is varied between 2.1 GeV and 3.85 GeV. Scaling when the lattice spacing is varied is very well sati sfied. The resulting flavorless conventional two loop Lambda(c)/MS is estim ated to be, respectively for the MOM and M (O) over tilde M scheme, 361(6) MeV and 345(6) MeV, while the three loop results are, depending on beta(2): Lambda(3)/MS = (412-59 beta(2)/beta(2,<(MS)over bar>) +/- 6 MeV) and Lambd a(3)/MS = (382 - 46 beta(2)/beta(2,<(MS)over bar>) +/- 5 MeV). A preliminar y computation of beta 2 in the M (O) over tilde M scheme leads to Lambda(3) /MS = 303(5) a(-1)(beta=6.0)/1.97GeV MeV.