The match between the ISAAC filters (J, H and Ks) and those used to establish the faint IR standard star system of Persson et al. (AJ, 116, 2475) are quite good, so we expect the colour terms to be small. If the zero point is expressed in the form
where is the ISAAC instrumental magnitude, is the catalogue magnitude and, for simplicity, we have ignored extinction, we expect that a will differ from 0 by less than 0.01 for X being one of J, H or Ks. The Js filter of ISAAC has a slightly redder effective wavelength than J, so we expect a non-negligible colour term. Theoretically, we expect a=-0.04.
However, the colour transformation between ISAAC magnitudes and those of LCO have never been experimentally verified, so the results quoted here should be considered with this in mind.