Trisections and cubes in elliptic curves

We show how to compute the pre-images of multiplication by 3 in group points an elliptic curve E over a field k characteristic different from 2 and such that E[3](k)=E[3]. Q=(xQ,yQ)∈[3]E(k) if only yQ−d−m(xQ−c) is cube for every 3-torsion point (c,d)∈E[3], where m slope tangent at (c,d). reduce our problem computation most independent cubic roots plus few polynomial operations.