  The weight two Eisenstein series may be considered as the first example of a
Katz $p$-adic modular form. Classically, its values are defined for the primes
of ordinary reduction. We offer a modified definition which applies uniformly
to all primes of good reduction, both ordinary and supersingular. We show that,
in the case of complex multiplication, these $p$-adic values coincide with the
algebraic value of this Eisenstein series.
