The Type Ia supernova (SN Ia) LSQ14fmg exhibits exaggerated properties which may help to reveal the origin of the super-Chandrasekhar (or 03fg-like) group. The optical spectrum is typical of a 03fg-like SN Ia, but the light curves are unlike those of any SNe Ia observed. The light curves of LSQ14fmg rise extremely slowly. At -23 rest-frame days relative to B-band maximum, LSQ14fmg is already brighter than $M_V$=-19 mag before host extinction correction. The observed color curves show a flat evolution from the earliest observation to approximately one week after maximum. The near-infrared light curves peak brighter than -20.5 mag in the J and H bands, far more luminous than any 03fg-like SNe Ia with near-infrared observations. At one month past maximum, the optical light curves decline rapidly. The early, slow rise and flat color evolution are interpreted to result from an additional excess flux from a power source other than the radioactive decay of the synthesized $^{56}Ni$. The excess flux matches the interaction with a typical superwind of an asymptotic giant branch (AGB) star in density structure, mass-loss rate, and duration. The rapid decline starting at around one month past B-band maximum may be an indication of rapid cooling by active carbon monoxide (CO) formation, which requires a low temperature and high density environment. These peculiarities point to an AGB progenitor near the end of its evolution and the core degenerate scenario as the likely explosion mechanism for LSQ14fmg.
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