Computing L-Polynomials of Picard curves from Cartier-Manin matrices

Sualeh Asif, Francesc Fité, Dylan Pentland

We study the sequence of zeta functions $Z(C_p,T)$ of a generic Picard curve $C:y^3=f(x)$ defined over $\mathbb{Q}$ at primes $p$ of good reduction for $C$. We define a degree 9 po…