This paper presents a formalism to characterize the redshift evolution of the dark energy potential. The method uses quantities similar to the Horizon-flow parameters in inflation and is general enough to handle multiscalar quintessence scenarios, exotic matter components, and higher-order curvature corrections to General Relativity. The shape of the dark energy potential can be recovered non-parametrically using this formalism, with approximations analogous to those in slow-roll inflation. However, current data do not allow a non-parametric and exact reconstruction of the potential, so a general parametric description is considered. This reconstruction can also be used in other approaches, such as the reconstruction of the redshift evolution of the dark energy equation of state $ w(z) $. Using observations of passively evolving galaxies and supernova data, constraints on the dark energy potential shape in the redshift range 0.1 < z < 1.8 are derived. The findings show that the potential is consistent with being constant at the 1σ level, although variations cannot be excluded with current data. Future data from the Atacama Cosmology Telescope are expected to greatly improve current constraints. The paper also discusses the reconstruction of the dark energy potential using Chebyshev polynomials and the constraints on the equation of state from current data. The results suggest that the dark energy potential is consistent with a cosmological constant at the 1σ level. The paper concludes that the dark energy potential is consistent with a cosmological constant equation of state (w = -1) in the redshift range 0.1 < z < 1.8.This paper presents a formalism to characterize the redshift evolution of the dark energy potential. The method uses quantities similar to the Horizon-flow parameters in inflation and is general enough to handle multiscalar quintessence scenarios, exotic matter components, and higher-order curvature corrections to General Relativity. The shape of the dark energy potential can be recovered non-parametrically using this formalism, with approximations analogous to those in slow-roll inflation. However, current data do not allow a non-parametric and exact reconstruction of the potential, so a general parametric description is considered. This reconstruction can also be used in other approaches, such as the reconstruction of the redshift evolution of the dark energy equation of state $ w(z) $. Using observations of passively evolving galaxies and supernova data, constraints on the dark energy potential shape in the redshift range 0.1 < z < 1.8 are derived. The findings show that the potential is consistent with being constant at the 1σ level, although variations cannot be excluded with current data. Future data from the Atacama Cosmology Telescope are expected to greatly improve current constraints. The paper also discusses the reconstruction of the dark energy potential using Chebyshev polynomials and the constraints on the equation of state from current data. The results suggest that the dark energy potential is consistent with a cosmological constant at the 1σ level. The paper concludes that the dark energy potential is consistent with a cosmological constant equation of state (w = -1) in the redshift range 0.1 < z < 1.8.