elegance has no recorded synonym. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is inelegance.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a refined quality of gracefulness and good taste
“she conveys an aura of elegance and gentility”
a quality of neatness and ingenious simplicity in the solution of a problem (especially in science or mathematics)
“the simplicity and elegance of his invention”
Synonyms, antonyms and the broader and narrower relations for elegance come from Princeton University’s WordNet. Full sources and licences.