The first resolved, multiply imaged supernova Type Ia, iPTF16geu, was observed 4 years ago, five decades after such systems were first envisioned. Because of the unique properties of the source, these systems hold a lot of promise for the study of galaxy structure and cosmological parameters. However, this very first example presented modelers with a few puzzles. It was expected that to explain image fluxes a contribution from microlensing by stars would be required, but to accommodate the magnitude of microlensing, the density slope of the elliptical power law lens model had to be quite shallow, $rho_{2D} propto r^{-0.7}$. Furthermore, the center of mass had to be displaced from that of observed light by ~0.1 kpc, and the position angle of light distribution was misaligned with that of mass by ~40 degrees. In this paper we present mass models that resolve the first two problems, and suggest a resolution of the third. Motivated by observations of local ellipticals, and some recent analysis of galaxy-scale lenses, our mass models consist of two offset (baryonic) mass components. The resulting mass distributions have a single centroid, but are lopsided, and have isodensity contours that are not purely elliptical and not self-similar with radius. For many of our models the microlensing requirements are modest, and the ring formed by the extended supernova host galaxy resembles the observed one.
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