Finding zeta function of an elliptic curve

332 Views Asked by At

Let $p \equiv 3 \pmod 4$ be a prime, and $E/F_{p^r}$ be the elliptic curve given by $y^2 = x^3 − x$. Find the zeta-function of $E/F_p$ and use it to determine $|E(F_{p^r} )|$ for all r>0.