The Jupiter Trojan asteroids are minor bodies that orbit 60 degrees before and 60 degrees behind Jupiter. Because these orbits are stable over the lifetime of the Solar System, the properties of these objects may inform us about the conditions under which the Solar System formed. We present BVRI photometry for 110 of the intrinsically brightest and presumably largest members of the L4 and L5 Jupiter Trojans. We use a new principal color component derived by Chatelain et al. (2016) that is indicative of taxonomic types relevant to the Jupiter Trojan asteroids. We find that 83% of the largest Jupiter Trojans are consistent with a D-type classification, while 17% show shallower slopes more consistent with X-type and C-type classifications. We show the L4 and L5 populations to be taxonomically indistinguishable at large sizes, as well as include findings about certain objects that have resulted from these data. Specifically, multi-filter light curves for twelve objects show signs of V-I color variation in as many as two thirds of these objects, and our richest datasets allow for the determination of phase curves and shapes for some asteroids including a new shape model and pole solution for (1173) Anchises. Our goal is to use this study to shed light on these fascinating objects and to place the Trojans in context in the larger Solar System.