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Observational data from space and ground-based campaigns reveal that the10-30 Ma old V1298 Tau star hosts a compact and massive system of four planets.Mass estimates for the two outer giant planets point to unexpectedly highdensities for their young ages. We investigate the formation of these twooutermost giant planets, V1298 Tau b and e, and the present dynamical state ofV1298 Tau's global architecture to shed light on the history of this young andpeculiar extrasolar system. We perform detailed N-body simulations to explorethe link between the densities of V1298 Tau b and e and their migration andaccretion of planetesimals within the native circumstellar disk. We combineN-body simulations and the normalized angular momentum deficit (NAMD) analysisto characterize V1298 Tau's dynamical state and connect it to the formationhistory of the system. We search for outer planetary companions to constrainV1298 Tau's architecture and the extension of its primordial circumstellardisk. The high densities of V1298 Tau b and e suggest they formed quite distantfrom their host star, likely beyond the CO$_2$ snowline. The higher nominaldensity of V1298 Tau e suggests it formed farther out than V1298 Tau b. Thecurrent architecture of V1298 Tau is not characterized by resonant chains.Planet-planet scattering with an outer giant planet is the most likely causefor the instability, but our search for outer companions using SPHERE and GAIAobservations excludes only the presence of planets more massive than 2M$_\textrm{J}$. The most plausible scenario for V1298 Tau's formation is thatthe system is formed by convergent migration and resonant trapping of planetsborn in a compact and plausibly massive disk. The migration of V1298 Tau b ande leaves in its wake a dynamically excited protoplanetary disk and creates theconditions for the resonant chain breaking by planet-planet scattering.

The GAPS program at TNG XLVII: The unusual formation history of V1298 Tau