Consider the conic C_d : x^2 - dy^2 = -1 to be solved in integers x and y. How often is C_d soluble as we vary over squarefree integers d? Stevenhagen conjectured an asymptotic formula, which was recently proved by Pagano and myself. The goal of this talk is to give a basic overview of the area such as class groups, genus theory and the Cohen--Lenstra heuristics. Speaker(s): Peter Koymans (University of Michigan)