When looking for synonyms for the phrase "so notorious," some words that come to mind are infamous, notorious, well-known, scandalous, and disreputable. All of these words have negative connotations and are associated with someone or something that has a bad reputation. Infamous suggests notoriety and a widespread negative reputation. Notorious implies a negative reputation but also carries the connotation of being well-known. Well-known can imply either a positive or negative reputation, but in the context of "so notorious," it would be synonymous with a negative reputation. Scandalous suggests something that has caused a scandal and is seen as unacceptable behavior. Lastly, disreputable suggests something not respected and is viewed negatively in society.