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We present extensive magnetic measurements of the(Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_{3}O_{y} (CLBLCO) system with its fourdifferent families (x) having a Tc^max(x) variation of 28% and minimalstructural changes. For each family we measured the Neel temperature, theanisotropies of the magnetic interactions, and the spin glass temperature. Ourresults exhibit a universal relation Tc=c*J*n_s for all families, where c~1, Jis the in plane Heisenberg exchange, and n_s is the carrier density. Thisrelates cuprate superconductivity to magnetism in the same sense that phononmediated superconductivity is related to atomic mass.Comment: With an additional inset in Fig.

Magnetic analog of the isotope effect in cuprates