  The Narasimhan-Nori conjecture asks for a closed formula for the number of
non-isomorphic principal polarizations of any given abelian variety. In this
paper, we introduce a new algorithm that gives a lower bound on the number of
non-isomorphic principal polarizations on any given abelian variety. We show,
for example, that the Jacobian of the genus four underlying curve of Schoen's
I-WP minimal surface has at least 9 non-isomorphic principal polarizations. We
also explore the Jacobians of Klein's quartic, Fermat's quartic, Bring's curve,
and more.
