I've seen several design variations of coaxial collinear antennas, and they can use 1/4 wave or 1/2 wave elements, and usually a combination of both. So, giving a simple answer with a number isn't really possible...
Consider that a collinear is basically phased 1/2 antennas placed end to end, and that a dipole is a single 1/2 antenna. So, a minimum sized collinear would have 2 half wave sections for 3 db gain. But depending on how you go about it, those two 1/2 antennas could be in 1/4 wave line sections.
All that said, the smallest I've seen is a 1/4 wave section on the bottom, one 1/2 section, then another 1/4 wave section, then a 1/4 wave whip on the top. Is that one element, three elements, or four? See the problem with your question?
