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Heusler compounds attract a great deal of attention from researchers thanks to a wealth of interesting properties, among which is superconductivity. Here we perform an extensive study of the superconducting and elastic properties of the cubic (full-)Heusler family using a mixture of ab initio methods, as well as interpretable and predictive machine-learning models. By analyzing the statistical distributions of these properties and comparing them to anti-perovskites, we recognize universal behaviors that should be common to all conventional superconductors while others turn out to be specific to the material family. In total, we discover a total of eight hypothetical materials with critical temperatures above 10 K to be compared with the current record of Tc = 4.7 K in this family. Furthermore, we expect most of these materials to be highly ductile, making them potential candidates for the manufacture of wires and tapes for superconducting magnets.