##1C = 1As##, i.e. Coulomb is defined by Ampère and time. I think a unit of elementary charge is usually defined positive in Coulomb whereas an electron carries the charge ##-1e##. It's a matter of taste and how much is the author willing to confuse his readers.
In particle physics you have the charge of an electron as elementary charge ##-1##, in electrodynamics its ##C>0##.