Congruences between Ramanujan's tau function and elliptic curves, and Mazur--Tate elements at additive primes

Anthony Doyon, Antonio Lei

We show that if $E/\mathbb{Q}$ is an elliptic curve with a rational $p$-torsion for $p=2$ or $3$, then there is a congruence relation between Ramanujan's tau function and $E$ modul…