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 Å ) 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 ^ { 56 } Ni and thus have a lower peak luminosity . 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 \pm 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 \pm 0.069 mag ) , corresponding to SN 2011fe having produced 38 % more ^ { 56 } Ni 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 .