Hasse's Theorem: min and max values with or without point of infinity? I have to calculate the min and max values of a field.
Min: $\lfloor{q+1-2 \sqrt{q}}\rfloor$
Max: $\lfloor{q+1+2 \sqrt{q}}\rfloor$
According to Hasse. BUT the exercise says that min and max should be found together with the point of infinity. So should I say min+1 and max+1?
Hope you get my question.

Hasse's theorem is usually stated as
$$ | \# E(\mathbb{F}_q) - (q + 1) | \leq 2\sqrt{q}$$
When we talk about the points on an elliptic curve $E/K$ where $K$ is a field, we are always talking about the points on the projective curve (that is, including the point at infinity). Thus if $E/\mathbb{F}_q$ is given by
$$f(x,y) = y^2 + a_1xy + a_3y - (x^3 + a_2x^2 + a_4x + a_6) = 0$$
when we talk about $E(\mathbb{F}_q)$ we really mean
$$\{(x,y) \in \mathbb{F}_q^2 : f(x,y) = 0 \} \cup \{(0:1:0)\}$$
