ag.algebraic geometry - [Solved] Multiplicity of a Poincaré divisor at the points of order 2

Let $X$ an abelian variety /$k$, char($k$)=0, $k=overline k$, and be $widehat{X}$ its dual. With $P$ I will denote the (normalized) Poincaré bundle over $Xtimes_kwidehat X$. We have an action of $Z/2Z$ over the abelian variety $Xtimes_kwidehat X$, given by the product $itimes i$ of the two inversions. Since the $P$ is symmetric there is a unique isomorphism $rho:Plongrightarrow(itimes i)^*P$ such that $rho(0,widehat 0)=$ identity over $P(0,widehat 0)$. Given a point of order 2 $(x,alpha)in Xtimes_kwidehat X$ one can define $e(x,alpha)$ as the scalar quantity, $a$ such that $rho(x,alpha)$ is given by multiplication by $a$. This is either 1 or -1.
My question is:
Is there a quick way to find the quantity $e(x,alpha)$ for the points of the form (x,widheat 0) with $x$ a point of order two? Could it be that it is always 1?

I know from Mumford (On the equation defining abelian varieties I, Proposition 2 pg 307) that if $D$ is a symmetric divisor such that $P=O_X(D)$ then
$$e(x,alpha)=(-1)^{m(x,alpha)-m(0,widehat 0)}$$
where $m(x,alpha)$ denote the multiplicity on $D$ at $(x,alpha)$. What I do not know is how a symmetric divisor $D$ such that $P=O_X(D)$ looks like and, moreover how to compute its multiplicity in the point of order two.

Thank you very much for all the answer I will receive!
Stgemain