  In this paper we relate some classical normal forms for complex elliptic
curves in terms of 4-point sets in the Riemann sphere. Our main result is an
alternative proof that every elliptic curve is isomorphic as a Riemann surface
to one in the Hesse normal form. In this setting, we give an alternative proof
of the equivalence between the Edwards and the Jacobi normal forms. Also, we
give a geometric construction of the cross ratios for 4-point sets in general
position.
