Birational invariants for the torus without affect in a group of $F_4$ type

In the paper all the cohomological birational invariants for the torus without affect in a semisimple exceptional group of $F_4$ type are calculated. Kunyavski B. and Cortella A. have proved that this torus is not rational. We prove that the Picard group of a projective model for the studied torus is not cohomologically trivial. We find all the subgroups in Weyl group $W(F_4)$ for which the corresponding cohomological invariant is not trivial.