  The Type Ia supernovae (SNe Ia) 2011by, hosted in NGC 3972, and 2011fe,
hosted in M101, are optical "twins," having almost identical optical
light-curve shapes, colours, and near-maximum-brightness spectra. However, SN
2011fe had significantly more ultraviolet (UV; 1600 < lambda < 2500 A) flux
than SN 2011by before and at peak luminosity. Theory suggests that SNe Ia with
higher progenitor metallicity should (1) have additional UV opacity near peak
and thus lower UV flux; (2) have an essentially unchanged optical
spectral-energy distribution; (3) have a similar optical light-curve shape; and
(4) because of the excess neutrons, produce more stable Fe-group elements at
the expense of radioactive 56Ni and thus have a lower peak luminosity. Foley &
Kirshner (2013) suggested that the difference in UV flux between SNe 2011by and
2011fe was the result of their progenitors having significantly different
metallicities. The SNe also had a large, but insignificant, difference between
their peak absolute magnitudes (Delta M_V, peak = 0.60 +/- 0.36 mag), with SN
2011fe being more luminous. We present a new Cepheid-based distance to NGC
3972, significantly improving the precision of the distance measurement for SN
2011by. With these new data, we determine that the SNe have significantly
different peak luminosities (Delta M_V, peak = 0.335 +/- 0.069 mag),
corresponding to SN 2011fe having produced 38% more 56Ni than SN 2011by, and
providing additional evidence for progenitor metallicity differences for these
SNe. We discuss how progenitor metallicity differences can contribute to the
intrinsic scatter for light-curve-shape-corrected SN luminosities, the use of
"twin" SNe for measuring distances, and implications for using SNe Ia for
constraining cosmological parameters.
