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The infinite-layer cuprate superconductors are the prototypical material family for exploring unconventional superconductivity and correlated electronic phenomena. We present a numerical study using the dynamical vertex approximation [1] of a three-band Emery model [2] that goes beyond the one-band Hubbard description. We find (i) a pseudogap [3] and (ii) a strong dependence of the band structure and superconducting dome on long-range hoppings. Neglecting these hoppings shifts the dome and yields a modulated d-wave gap, whereas including them restores a conventional d-wave gap and places the dome in the correct doping range. Funding by the Austrian Science Fund (FWF) through Grant DOI 10.55776/I5398 (DFG Project No. 465000489) is gratefully acknowledged. [1] G. Rohringer et al., Rev. Mod. Phys. 90, 025003 (2018). [2] V. J. Emery, Phys. Rev. Lett. 58, 2794 (1987). [3] M. O. Malcolms et al., arXiv:2412.14951 (2024).