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X(1), X(4), X(80), X(484), X(502), X(517), X(1263), X(2687) 

K682 is a FuhrmannFeuerbach cubic, see details at K681 and also K529, K683, K684, K685. K682 is a cubic with focus X(5). It has three asymptotes concurring at X(5) but one only is real, namely the line X(5)X(517), which is also the orthic line of the cubic. K682 and K001 meet at 9 identified points, in particular X(1), X(4), X(484), X(1263). 
