Regulator Indecomposable Cycles on a Product of Elliptic Curves We provide a novel proof of the existence of regulator indecomposables in the cycle group $CH^2(X,1)$, where $X$ is a sufficiently general product of two elliptic curves. In particular, the nature of our proof provides an illustration of Beilinson rigidity. Keywords:real regulator, regulator indecomposable, higher Chow group, indecomposable cycleCategory:14C25