When Constantine wanted to strengthen his bonds with the other Tetrarchs, in 307 AD he married Fausta, the daughter of the emperor Maximian.
[1][2] Barnes, Woods and the PLRE view the panegyric as proof that she was married to Constantine,[3][4][2] while Pohlsander considers the possibility of the panegyrist not being entirely truthful.
The offspring of an illegitimate affair could have caused dynastical problems and would likely be dismissed, but Crispus was raised by his father in Gaul.
Constantine's father later had to divorce her for political reasons, specifically, to marry Flavia Maximiana Theodora, the daughter of Maximian, in order to secure his alliance with his new father-in-law.
Constantine even entrusted his education to Lactantius, among the most important Christian teachers of that time, who probably started teaching Crispus before 317.