Question: Designating names to points in a plot

I have some elliptic curve with some points on it:

I would like to give the points some names, P, etc., but cannot figure out how to do that probably simple task. The help pages ?plot,options and ?pointplot do not seem to cover it; I may be mistaken, of course. The above plot is the result of the following code:

curve := y^2 = x^3 - 43*x + 166;
   plot(+sqrt(rhs(curve)),x = -10..12),
   plot(-sqrt(rhs(curve)),x = -10..12),
   pointplot([[3,8],[-5,16],[11,32],[3,-8]],symbol = solidbox)

Update: Using, among other things, the textplot command as suggested below, here, just for the fun of it, a plot illustrating the group 'addition' of points on an elliptic curve, the three lines being tangents to the curve:

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