What is "eigencurve"

n. (context mathematics number theory English) A rigid analytic curve that parametrizes certain ''p''-adic families of modular forms.

In number theory, an eigencurve is a rigid analytic curve that parametrizes certain p-adic families of modular forms, and an eigenvariety is a higher-dimensional generalization of this. Eigencurves were introduced by , and the term "eigenvariety" seems to have been introduced around 2001 by .