Abelian varieties with elliptic subgroups provide cycles on the moduli space of principally polarized abelian varieties. Even though the cycles are in general non-tautological, the relations between them has a very rich structure, conjecturally governed by modular forms. I will explain this conjecture, what we can prove about it, and its relation with the moduli space of curves and Gromov-Witten theory. If time permits, I will explain possible extensions of these results to the boundary.