While the kinematics of galaxies up to z~3 have been characterized in detail, only a handful of galaxies at high redshift (z>4) have been examined in such a way. The Atacama Large Millimeter/submillimeter Array (ALMA) Large Program to INvestigate [CII] at Early times (ALPINE) survey observed a statistically significant sample of 118 star-forming main sequence galaxies at z=4.4-5.9 in [CII]158um emission, increasing the number of such observations by nearly 10x. A preliminary qualitative classification of these sources revealed a diversity of kinematic types (i.e., rotators, mergers, and dispersion-dominated systems). In this work, we supplement the initial classification by applying quantitative analyses to the ALPINE data: a tilted ring model (TRM) fitting code (3DBarolo), a morphological classification (Gini-M20), and a set of disk identification criteria. Of the 75 [CII]-detected ALPINE galaxies, 29 are detected at sufficient significance and spatial resolution to allow for TRM fitting and the derivation of morphological and kinematic parameters. These 29 sources constitute a high-mass subset of the ALPINE sample (M_*>10^9.5Msol). We robustly classify 14 of these sources (six rotators, five mergers, and three dispersion-dominated systems); the remaining sources showing complex behaviour. By exploring the G-M20 of z>4 rest-frame FIR and [CII] data for the first time, we find that our 1~6kpc resolution data alone are insufficient to separate galaxy types. We compare the rotation curves and dynamical mass profiles of the six ALPINE rotators to the two previously detected z~4-6 unlensed main sequence rotators, finding high rotational velocities (~50-250km/s) and a diversity of rotation curve shapes.
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