  We use machine learning to study the locus ${\mathcal L}_n$ of genus two
curves with $(n, n)$-split Jacobian. More precisely we design a transformer
model which given values for the Igusa invariants determines if the
corresponding genus two curve is in the locus ${\mathcal L}_n$, for $n=2, 3, 5,
7$. Such curves are important in isogeny based cryptography.
  During this study we discover that there are no rational points ${\mathfrak
p} \in {\mathcal L}_n$ with weighted moduli height $\leq 2$ in any of
${\mathcal L}_2$, ${\mathcal L}_3$, and ${\mathcal L}_5$. This extends on
previous work of the authors to use machine learning methods to study the
moduli space of genus 2 algebraic curves.
