  Supermassive black holes (SMBHs) are a key catalyst of galaxy formation and
evolution, leading to an observed correlation between SMBH mass $M_{\rm BH}$
and host galaxy velocity dispersion $\sigma_{\rm e}$. Outside the local
Universe, measurements of $M_{\rm BH}$ are usually only possible for SMBHs in
an active state: limiting sample size and introducing selection biases.
Gravitational lensing makes it possible to measure the mass of non-active
SMBHs. We present models of the $z=0.169$ galaxy-scale strong lens Abell~1201.
A cD galaxy in a galaxy cluster, it has sufficient `external shear' that a
magnified image of a $z = 0.451$ background galaxy is projected just $\sim 1$
kpc from the galaxy centre. Using multi-band Hubble Space Telescope imaging and
the lens modeling software $\texttt{PyAutoLens}$ we reconstruct the
distribution of mass along this line of sight. Bayesian model comparison
favours a point mass with $M_{\rm BH} = 3.27 \pm 2.12\times10^{10}\,$M$_{\rm
\odot}$ (3$\sigma$ confidence limit); an ultramassive black hole. One model
gives a comparable Bayesian evidence without a SMBH, however we argue this
model is nonphysical given its base assumptions. This model still provides an
upper limit of $M_{\rm BH} \leq 5.3 \times 10^{10}\,$M$_{\rm \odot}$, because a
SMBH above this mass deforms the lensed image $\sim 1$ kpc from Abell 1201's
centre. This builds on previous work using central images to place upper limits
on $M_{\rm BH}$, but is the first to also place a lower limit and without a
central image being observed. The success of this method suggests that surveys
during the next decade could measure thousands more SMBH masses, and any
redshift evolution of the $M_{\rm BH}$--$\sigma_{\rm e}$ relation. Results are
available at https://github.com/Jammy2211/autolens_abell_1201.
