LetU=U(sl2)⊗nbe the tensor power of n copies of the enveloping algebraU(sl2) over an arbitrary fieldKof characteristic zero. In this paper we list the prime ideals ofUby generators and classify them by height. IfZis the center ofUandJis a prime ideal ofZ, there are exactly 25prime idealsIofUwithI∩Z=J, where 0 ≤ s = s(J) ≤ n is an integer. Indeed, with respect to inclusion, they form a lattice isornorphic to the lattice of subsets of a set. WhenJis a maximal ideal ofZ, there are only finitely many two-sided ideals ofUcontainingJ, They are presented by generators and their lattice is described, In particular, for each suchJthere exists a unique maximal ideal ofUcontainingJand a unique ideal ofUminimal with respect to the property that it properly containsJU. Similar results are given in the case whenUis the tensor product of infinitely many copies ofU(sl2).