et $e$ be an elliptic curve defined over a number field $k$ and $f$ a finite cyclic extension of $k$ of $p$-power degree for an odd prime $p$. under certain technical hypotheses, we describe a reinterpretation of the equivariant tamagawa number conjecture (`etnc') for $e$, $f/k$ and $p$ as an explicit family of $p$-adic congruences involving values of derivatives of the hasse-weil $l$-functions of twists of $e$, normalised by completely explicit twisted regulators. this reinterpretation makes the etnc amenable to numerical verification and furthermore leads to explicit predictions which refine well-known conjectures of mazur and tate. this is a report on joint work with daniel macias castillo