  How magnetic energy is injected and released in the solar corona, keeping it
heated to several million degrees, remains elusive. Coronal heating generally
increases with increasing magnetic field strength. From comparison of a
non-linear force-free model of the three-dimensional active-region coronal
field to observed extreme-ultraviolet loops, we find that (1) umbra-to-umbra
coronal loops, despite being rooted in the strongest magnetic flux, are
invisible, and (2) the brightest loops have one foot in an umbra or penumbra
and the other foot in another sunspot's penumbra or in unipolar or
mixed-polarity plage. The invisibility of umbra-to-umbra loops is new evidence
that magnetoconvection drives solar-stellar coronal heating: evidently the
strong umbral field at \underline{both} ends quenches the magnetoconvection and
hence the heating. Broadly, our results indicate that, depending on the field
strength in both feet, the photospheric feet of a coronal loop on any
convective star can either engender or quench coronal heating in the loop's
body.
