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We are witnessing a great transition towards a society powered by renewable energies to meet the ever-stringent climate target. Hydrogen, as an energy carrier, will play a key role in building a climate-neutral society. Although liquid hydrogen is essential for hydrogen storage and transportation, liquefying hydrogen is costly with the conventional methods based on Joule-Thomas effect. As an emerging technology which is potentially more efficient, magnetocaloric hydrogen liquefaction is a "game-changer". In this work, we have investigated the rare-earth-based Laves phases ${\rm R}Al_2$ and ${\rm R}Ni_2$ for magnetocaloric hydrogen liquefaction. We have noticed an unaddressed feature that the magnetocaloric effect of second-order magnetocaloric materials can become "giant" near the hydrogen boiling point. This feature indicates strong correlations, down to the boiling point of hydrogen, among the three important quantities of the magnetocaloric effect: the maximum magnetic entropy change $\Delta S_{m}^{max}$, the maximum adiabatic temperature change $\Delta T_{ad}^{max}$, and the Curie temperature $T_C$. Via a comprehensive literature review, we interpret the correlations for a rare-earth intermetallic series as two trends: (1) $\Delta S_{m}^{max}$ increases with decreasing $T_C$; (2) $\Delta T_{ad}^{max}$ decreases near room temperature with decreasing $T_C$ but increases at cryogenic temperatures. Moreover, we have developed a mean-field approach to describe these two trends theoretically. The dependence of $\Delta S_{m}^{max}$ and $\Delta T_{ad}^{max}$ on $T_C$ revealed in this work helps us quickly anticipate the magnetocaloric performance of rare-earth-based compounds, guiding material design and accelerating the discoveries of magnetocaloric materials for hydrogen liquefaction.