Blazon: Per fess argent a cross of Calatrava gules and azure a tower of the first
Whatever kind of shade some ancient writers throw on canting arms, I love them. It’s like all the best parts of puns and linguistics put together! It’s especially satisfying when every element of the arms matches a component of the name in question. The “de Calatrava” clearly corresponds to the cross of Calatrava, from the military order that occupied much of the south of Spain during Reconquista. The first part of the name is covered in the base half of the arms – “torre alba” being a rather poetic way of saying “white tower” in Spanish. It’s possible the white tower in question is a direct reference to the town’s old fortress (which had a church built on it more than 500 years ago), but that’s pure speculation.