  The observational cosmology with distant Type Ia supernovae (SNe) as standard
candles claims that the Universe is in accelerated expansion, caused by a large
fraction of dark energy. In this paper we investigate the SN Ia environment,
studying the impact of the nature of their host galaxies on the Hubble diagram
fitting. The supernovae (192 SNe) used in the analysis were extracted from
Joint-Light-curves-Analysis (JLA) compilation of high-redshift and nearby
supernovae which is the best one to date. The analysis is based on the
empirical fact that SN Ia luminosities depend on their light curve shapes and
colors. We confirm that the stretch parameter of Type Ia supernovae is
correlated with the host galaxy type. The supernovae with lower stretch are
hosted mainly in elliptical and lenticular galaxies. No significant correlation
between SN Ia colour and host morphology was found.
  We also examine how the luminosities of SNe Ia change depending on host
galaxy morphology after stretch and colour corrections. Our results show that
in old stellar populations and low dust environments, the supernovae are
slightly fainter. SNe Ia in elliptical and lenticular galaxies have a higher
$\alpha$ (slope in luminosity-stretch) and $\beta$ (slope in luminosity-colour)
parameter than in spirals. However, the observed shift is at the 1-$\sigma$
uncertainty level and, therefore, can not be considered as significant.
  We confirm that the supernova properties depend on their environment and that
the incorporation of a host galaxy term into the Hubble diagram fit is expected
to be crucial for future cosmological analyses.
