  We enlarge the classes of inflaton and quintessence fields by generalizing
the pseudo Nambu--Goldstone boson potential by means of elliptic Jacobian
functions, which are characterized by a parameter $k$. We use such a
generalization to implement an inflationary era and a late acceleration of the
universe. As an inflationary model the Jacobian generalization leads us to a
number of e-foldings and a primordial spectrum of perturbations compatible with
the {\it Planck collaboration} 2015. As a quintessence model, a study of the
evolution of its equation of state (EoS) and its $w'$--$w$ plane helps us to
classify it as a thawing model. This allows us to consider analytical
approximations for the EoS recently discovered for thawing quintessence. By
using JLA Supernovae Ia and Hubble parameter $H(z)$ data sets, we perform an
observational analysis of the viability of the model as quintessence.
