We present the first time-simultaneous high angular resolution spectral energy distribution (SED) of the core of M87 at a scale of 0.4 arcsecs across the electromagnetic spectrum. Two activity periods of the core of M87 are sampled: a quiescent mode, representative of the most common state of M87, and an active one, represented by the outburst occurring in 2005. The main difference between both SEDs is a shift in flux in the active SED by a factor of about two, their shapes remaining similar across the entire spectrum. The shape of the compiled SEDs is remarkably different from those of active galactic nuclei (AGN). It lacks three major AGN features: the IR bump, the inflection point at about 1 micron and the blue bump. The SEDs also differ from the spectrum of a radiatively inefficient accretion flow. Down to the scales of ~12 pc from the centre, we find that the emission from a jet gives an excellent representation of the spectrum over ten orders of magnitude in frequency for both the active and the quiescent phases of M87. The inferred total jet power is one to two orders of magnitude lower than the jet mechanical energy inferred from various methods in the literature. This discrepancy cannot easily be ascribed to variability. Yet, our measurements regard the inner few parsecs which might provide a genuine account of the jet power at the base. We derive a strict upper limit to the accretion rate of 6 x 10E-5 Mo / yr, assuming 10% efficiency. The inferred accretion power can account for M87 radiative luminosity at the jet-frame assuming boosting factors larger than 10, it is however two orders of magnitude below that required to account for M87 jet kinetic power. We thus propose that energy tapped from the black hole spin may be a complementary source to power the jet of M87, a large supply of accreting gas becoming thus unnecessary.