  We show that the $p$-adic completion of any affine elliptic curve with
ordinary reduction possesses Frobenius lifts whose "normalized" action on
$1$-forms preserves mod $p$ the space of invariant $1$-forms. We next show
that, after removing the $2$-torsion sections, the above situation can be
"infinitesimally deformed" in the sense that the above mod $p$ result has a mod
$p^2$ analogue. While the "eigenvalues" mod $p$ are given by the reciprocal of
the Hasse polynomial, the "eigenvalues" mod $p^2$ are given by an appropriate
$\d$-modular function whose reciprocal is a $p$-adic deformation of the Hasse
polynomial.
