number points and twist of elliptic curve

number points and twist of elliptic curve

Let elliptic curve $y^2 = x^3 + 1$ has ($q^2 + 2q + 1$)
$\mathbb{F}_{q^2}$-rational points.
Let $\zeta$ is generator of $\mathbb{F}_{q^2}^*/\mathbb{F}_{q^2}^{*6}$.
Curve $E'$ with equation $y^2 = x^3 + \zeta$ has ($q^2 + q +1$)
$\mathbb{F}_{q^2}$-rational
points(http://www.math.brown.edu/~reinier/supersingular.pdf). Why?