What does the L-function of $x^4+y^4=z^4$ look like?

For the Fermat curve $x^4+y^4=z^4$, what does its L-function look like? I know its zeta function over prime $p$ should have the form $\frac{P_p(t)}{(1-t)(1-pt)}$, with $P_p$ a polynomial of degree $6$. The L-function should be $\prod_p P_p(t)^{-1}$, right? I think the only possible bad primes are $2$ and $3$, so what should its conductor be?