What is the sign of an infinite prime?
I'm reading ch. II of Silverman's Advanced Topics in the Arithmetic of Elliptic Curves without a background in class field theory. On the bottom of page 155, Silverman writes $\text{sign}(N_s)=\text{sign}(s_\infty)$ and I am unclear on what is meant here.
Further, if anybody is feeling up to it, does the sign of an infinite prime relate to the reciprocity map, and if so how? Thank you in advance.
For the benefit of other confused grad students, I will further explain my confusion. I'm essentially restating reuns answer in less precise terms.
In Advanced Topics in the Arithmetic of Elliptic Curves we are considering an idele $s\in \mathbb{A}_\mathbb{Q}^*$. There is only one real place and we require $N_s$ has the same sign as $s_\infty$, the entry in the component of $s$ representing the real place.
Generally, we don't allow a modulus to contain any complex places, so we don't need to worry about them. Intuitively, $\text{sign}(α)$ being positive is the equivalent of $\alpha$ being congruent to 1 modulo $\mathfrak{p}^{v_\mathfrak{p}(\mathfrak{m})}$ where $\mathfrak{p}$ is a prime ideal and $\mathfrak{m}$ is our modulus.
I found Sutherland's notes http://math.mit.edu/classes/18.785/2015fa/LectureNotes20.pdf to be very concise and helpful.