  The superconducting parameters are the key for building or identifying the
theory responsible for the mechanism of superconductivity. Such parameters for
fulleride superconductors have not been well established despite the tremendous
efforts over the past 30 years. Here we provide a full set of parameters
through a systematic study on a well-characterized K$_{3}$C$_{60}$ sample. The
obtained high upper critical field of 33.0$\pm$0.5 T from the direct electrical
transport measurements together with the relatively high critical temperature
and large critical current density classifies K$_{3}$C$_{60}$ as a promising
three-dimensional superconducting magnet material with the advantage of the
rich carbon abundance on the Earth. This high upper critical field along with
the large reduced superconducting energy gap and strong phonon self-energy
effect supports the strong electron-phonon coupling interactions in this
superconductor. The evaluation of all self-consistently obtained parameters
suggests the unconventional nature of the superconductivity for K$_3$C$_{60}$
with the joint contributions from the strong electron-phonon coupling and
electron correlations. These results and findings are important not only for
fundamentally understanding the superconductivity in fullerides but also for
future superconducting magnet developments and applications.
