We perform statistical analysis of solar flare light curves and ribbon morphology to advance our understanding of flare impulsiveness, an important parameter to describe stellar flares. The Solar Dynamics Observatory Extreme Ultraviolet Variability Experiment (SDO/EVE) provides “Sun-as-a-star” data corresponding to the variability of the Sun’s irradiance in the XUV and EUV wavelengths (from 0.1 to 106 nm). Using EVE light curves in the 304 Angstrom line, we study 2049 solar flares from 30 April 2010 to 26 May 2014. We present an algorithm for fitting the flare light curves in the 304 Angstrom line, emitted by He II at around 50000 K from the chromosphere and transition region and therefore representative of the dominant source of radiation in a solar flare. We use this algorithm to identify particularly high signal-to-noise flare light curves within the database, with representatives from C, M, and X flare classes. The parameters of the model associated with each flare can be used to identify notable features such as the incidence of multiple peaks in the rise phase. Identification of the rise and decay phases for each flare allows us to compare rise phase duration and flare impulsiveness to geometrical and physics-based properties of each flare, an important step in advancing our understanding of flare energy release. Specifically, using SDO Atmospheric Imaging Assembly (SDO/AIA) instrument data in the 1600 Angstrom line, we analyze the flare morphology and energy release in the context of the “impulsiveness” classification scheme for a sub-sample of the flares. We also compare this index to several solar flare properties including duration, peak X-ray flux, reconnection rate, and quasi-periodic pulsation (QPP) period, among others.