Using a sample of 208 broad-line active galactic nuclei (AGNs) from the Swift/BAT AGN Spectroscopic Survey in the ultra-hard X-ray band (14-195keV), the hot corona properties are investigated, i.e. the fraction of gravitational energy dissipated in the hot corona and the hard X-ray photon index. The bolometric luminosity, L_Bol_, is calculated from host-corrected luminosity at 5100{AA}. Virial supermassive black-hole masses (SMBH, M_BH_) are calculated from the H{beta} line width and the corresponding broad-line region size-luminosity empirical relation at 5100{AA}. We find a strong anti-correlation between the fraction of energy released in corona (F_X_=L_14-195keV_/L_Bol_) and the Eddington ratio ({epsilon}=L_Bol_/L_Edd_), F_X_{prop.to}{epsilon}^-0.60+/-0.1^. It is found that this fraction also has a correlation with the SMBH mass, F_X_{prop.to}{epsilon}^-0.74+/-0.14^M_BH_^-0.30+/-0.03^. Assuming that magnetic buoyancy and field reconnection lead to the formation of a hot corona, our result favours the shear stress tensor being a proportion of the gas pressure. For our entire sample, it is found that the hard X-ray photon index {Gamma} has a weak but significant correlation with the Eddington ratio, {Gamma}=2.17+0.21log{epsilon}. However, this correlation is not robust because the relation is not statistically significant for its subsample of 32 reverberation-mapping AGNs with relatively reliable M_BH_ or its subsample of 166 AGNs with single-epoch M_BH_. We do not find a statistically significant relation between the photon index and the Eddington ratio taking into account an additional dependence on F_X_.