Picard groups of some local categories

For each p-local spectrum E, L-E denotes the full subcategory consisting of E-local spectra of the category of p-local spectra. The Picard group Pic(L-E) is the collection of isomorphism classes of invertible spectra in LE. If this is a set, it is a group with multiplication defined by the smash product. We show that if a spectrum E satisfies a relation < E > >= (HZ/p) of the Bousfield classes, then Pic(L-E) = Z. In particular, Pic(L-E) = Z if E is connective.