  We propose a model for leptons based on the smallest modular finite group
$\Gamma_2\cong S_3$ that, for the first time, accounts for both the hints of
large low-energy CP-violation in the lepton sector and the matter-antimatter
asymmetry of the Universe, generated by only two heavy right-handed neutrinos.
These same states are also employed in a Minimal seesaw mechanism to generate
light neutrino masses. Besides the heavy neutrinos, our particle content is the
same as the Standard Model (SM), with the addition of one single modulus
$\tau$, whose vacuum expectation value is responsible for both the modular and
CP-symmetry breakings. We show that this minimalistic SM extension is enough to
get an excellent fit to low energy neutrino observables and to the required
baryon asymmetry $\eta_B$. Predictions for the neutrino mass ordering,
effective masses in neutrinoless double beta decay and tritium decay as well as
for the Majorana phases are also provided.
