  Using JWST observations of a primary transit and two secondary eclipses for
GJ 1214b, we determine an eccentricity that is more precise than a decade of
HARPS data, which enables us to measure the stellar density to 2.62%. Coupled
with a prior on the stellar mass from a dynamically calibrated K-$M_*$
relation, we determine $R_*$ to 1.13% -- 3 times more precise than any other
published analysis of this system. Then, using the bolometric flux from an
spectral energy distribution model, we determine $T_{\rm eff}$ to 1.39% -- 40%
more precise than systematic floors from spectroscopy. Within the global model,
these also improve the planetary radius and insolation. This is a proof of
concept for a new method to determine accurate $R_*$ and $T_{\rm eff}$ to a
precision currently achieved for only a small number of low-mass stars. By
applying our method to all high signal-to-noise ratio planetary transits and
occultations, we can expand the sample of precisely measured stars without
assuming tidal circularization and calibrate new relations to improve our
understanding of all low-mass stars.
