Summary: Let \(\tau\) be a point in the upper half-plane such that the elliptic curve corresponding to \(\tau\) can be defined over \(\mathbb{Q}\), and let \(f\) be a modular form on the full modular group with rational Fourier coefficients. By applying the Ramanujan differential operator \(D\) to \(f\), we obtain a family of modular forms \(D^lf\). In this paper we study the behavior of \(D^l(f)(\tau)\) modulo the powers of a prime \(p > 3\). We show that for \(p \equiv 1 \bmod 3\) the quantities \(D^l(f)(\tau)\), suitably normalized, satisfy Kummer-type congruences, and that for \(p \equiv 2 \bmod 3\) the \(p\)-adic valuations of \(D^l(f)(\tau)\) grow arbitrarily large. We prove these congruences by making a connection with a certain elliptic curve whose reduction modulo \(p\) is ordinary if \(p \equiv 1 \bmod 3\) and supersingular otherwise.