Helium-4 is famous for its ability to form a Bose-Einstein condensate (BEC), because the atom is, in its ground state, a boson. This happens because the number of protons equals the number of neutrons and they're both even. The next atom for which this should be true would be Beryllium-8, but it has an absurdly short half-life. That leaves us with carbon-12 being the next lightest atom that should be a boson in its ground state.
Before today, I'd only ever heard of of BECs formed by helium and photons. Wikipedia's Bose-Einstein condensate article also lists rubidium-87 and sodium-23. That makes it look like the requirement for the individual atoms to be bosons may not actually be a requirement, and may even be a disadvantage since it lowers the cross-section for laser cooling.
Regardless, under what conditions should carbon-12 form a BEC? The only mention of carbon-12 BECs I find in the literature, that isn't about atomic physics, is the statement, "While a BEC of carbon-12 is not practical[...]," in the context of using carbon-12 in defining Avogadro's number in Appendix B of this paper about using properties of BECs to measure the mass of atoms. This statement has no other qualifications, so I assume that the difficulties are considered to be textbook level knowledge in the field.
The critical temperature formula in Wikipedia's article $$ T_c = \frac{2\pi\hbar^2}{m k_B} \left(\frac{n}{\zeta(3/2)}\right)^{2/3} $$ is derived under the assumption that the particles are in a non-interacting gas. Is that the problem that makes carbon-12 difficult to get into a BEC? That is, is the problem that to get carbon-12 to not strongly interact $n$ must be very low, making $T_c$ impractically low for an atom that (I assume) can't be easily laser cooled? I would assume that rubidium-87 and sodium-23 have similar problems, so is it something else?