The modern system treats eleven as the first master number, unreducible and charged with heightened intuition. That doctrine is twentieth century and American, and it is worth setting beside what eleven meant before anyone thought of it that way, because the older readings run in the opposite direction.
Ancient and medieval writers who bothered with eleven at all treated it as excess. Ten was the complete count, the number of fingers and of the commandments, and eleven was what fell past the edge of a finished set without being enough to make a new one. Latin Christian exegesis used it that way for transgression: a number that has left completeness behind and arrived nowhere.
The clearest scriptural instance makes the same point without any commentary. After Judas, the apostles number eleven, and the opening chapter of Acts treats that as a defect requiring immediate repair. Lots are cast, Matthias is chosen, and the twelve is restored before anything else can proceed. Eleven there is not a heightened state. It is a gap in a structure.
Arithmetically it is awkward in ways the older systems noticed. It is the first two-digit prime, it fits none of the neat figurate families, and in a base-ten world it is the first number whose written form repeats a digit without meaning anything by it.
The modern rehabilitation reverses all of this by fiat rather than by argument. No ancient authority treats any two-digit number as unreducible, because no ancient authority reduces numbers in the first place.