  We prove identifiability of the tree parameters of the 3-class Jukes-Cantor
mixture model. The proof uses ideas from algebraic statistics, in particular:
finding phylogenetic invariants that separate the varieties associated to
different triples of trees; computing dimensions of the resulting phylogenetic
varieties; and using the disentangling number to reduce to trees with a small
number of leaves. Symbolic computation also plays a key role in handling the
many different cases and finding relevant phylogenetic invariants.
