This work studies the enumeration of answers to conjunctive queries. Research on this topic typically focuses on conjunctive queries without self-joins. We want to work towards a dichotomy that allows us to know if a conjunctive query with self-joins can be enumerated with optimal time guarantees: linear time before the first answer and constant delay between answers. In this work, we have found a sufficient and necessary conditions. However, we have examples that we can not classify and can lead to new work on the subject.