We reprove here the smoothness and the irreducibility of the quadratic dynatomic curves (c; z) 2 C2 j z is n-periodic for z2 + c . The smoothness is due to Douady-Hubbard. Our proof here is based on elementary calculations on the pushforwards of speci c quadratic di erentials, following Thurston and Epstein. This approach is a computational illustration of the power of the far more general transversality theory of Epstein. The irreducibility is due to Bousch, Morton and Lau-Schleicher with di erent ap- proaches. Our proof is inspired by the proof of Lau-Schleicher. We use elementary combinatorial properties of the kneading sequences instead of internal addresses
