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The gamma-ray emitting galaxy SBS 0846+513 has been classified as a Narrow-Line Seyfert 1 from its spectroscopy, and on that basis it was thought likely to have a small central black hole hosted in a spiral galaxy. But very few of the gamma-ray Narrow-Line Seyfert 1s have high-resolution imaging of their hosts, so it is unknown how those expectations hold up for the gamma-emitting class. We have observed this galaxy in the J-band with the Large Binocular Telescope's LUCI1 camera and the ARGOS adaptive optics system. We estimate its black hole mass to lie between $7.70 \leq \log \frac{\text{M}}{\text{M}_\odot} \leq 8.19$, using the correlation with bulge luminosity, or $7.96 \leq \log \frac{\text{M}}{\text{M}_\odot} \leq 8.16$ using the correlation with Sérsic index, putting its mass at the high end of the Narrow Line Seyfert 1 range. These estimates are independent of the Broad Line Region viewing geometry and avoid underestimates due to looking down the jet axis. Its host shows evidence of a bulge + disc structure, both from two-dimensional modeling and isophote shape, in keeping with the expectations. Mergers and interactions appear to be common among the gamma-ray Narrow-Line Seyfert 1s, and we see some circumstantial evidence for companion galaxies or disturbed features in the host.