A polynomial $D(t)$ is called Pellian if the ring generated over $C[t]$ by its square root has non constant units. By work of Masser and Zannier on the relative Manin-Mumford conjecture for jacobians, separable sextic polynomials are usually not Pellian. The same applies in the non-separable case, though some exceptional families occur, in relation to Ribet sections on generalized jacobians.