AN OCTAHEDRAL-ELLIPTIC TYPE EQUALITY IN BR-2(K)

Let k be a field of characteristic not equal 2, 3 which does not conta in the cubic roots of unity. Given a quartic irreducible polynomial f is an element of k[x] with discriminant -3 in k/k-*(2) and Galois gro up S-4, we describe in a explicit way the equivalence between the obst ruction of a Galois embedding problem of octahedral type attached to S and the obstruction to the existence of an elliptic curve having the splitting field of f as field of x-coordinates of its 3-torsion points .