  The Hubble diagram (HD) is a plot that contains luminous distance modulus
presented with respect to the redshift. The distance modulus--redshift relation
of the most well-known ``standard candles'', the type Ia supernovae (SN), is a
crucial tool in cosmological model testing. In this work, we use the SN Ia data
from the Pantheon catalogue to calibrate the Swift long gamma-ray bursts
(LGRBs) as ``standard candles'' via the Amati relation. Thus, we expand the HD
from supernovae to the area of the Swift LGRBs up to $z\sim8$. To improve the
quality of estimation of the parameters and their errors, we implement the
Monte-Carlo uncertainty propagation method. We also compare the results of
estimation of the Amati parameters calibrated by the SN Ia, and by the standard
$\Lambda$CDM model and find no statistically significant distinguish between
them. Although the size of our LGRB sample is relatively small and the errors
are high, we find this approach of expanding the cosmological distance scale
perspective for future cosmological tests.
