  We used the GMBCG galaxy cluster catalogue and SDSS-II supernovae data with
redshifts measured by the BOSS project to identify 48 SNe Ia residing in rich
galaxy clusters and compare their properties with 1015 SNe Ia in the field.
Their light curves were parametrised by the SALT2 model and the significance of
the observed differences was assessed by a resampling technique. To test our
samples and methods, we first looked for known differences between SNe Ia
residing in active and passive galaxies. We confirm that passive galaxies host
SNe Ia with smaller stretch, weaker colour-luminosity relation [$\beta$ of
2.54(22) against 3.35(14)], and that are $\sim$ 0.1 mag more luminous after
stretch and colour corrections. We show that only 0.02 per cent of random
samples drawn from our set of SNe Ia in active galaxies can reach these values.
Reported differences in the Hubble residuals scatter could not be detected,
possibly due to the exclusion of outliers. We then show that, while most field
and cluster SNe Ia properties are compatible at the current level, their
stretch distributions are different ($\sim3\sigma$): besides having a higher
concentration of passive galaxies than the field, the cluster's passive
galaxies host SNe Ia with an average stretch even smaller than those in field
passive galaxies (at 95 per cent confidence). We argue that the older age of
passive galaxies in clusters is responsible for this effect since, as we show,
old passive galaxies host SNe Ia with smaller stretch than young passive
galaxies ($\sim4\sigma$).
