The sets of tables presented here were based on Adam Chalcrafts braid representations of knots and links. These braid representations use Rolfsens designation of knots where possible, and the enumerations in  otherwise. Information on the braid representations may be found at his website, including a list or corrections to  and an explanation of the extended designation.
The braid programme has been used to calculate Alexander polynomials for knots up to 11 crossings and links up to 10 crossings based on Adam Chalcraft's braid representations.
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 J.H. Conway, An enumeration of knots and links, and some of their algebraic properties, Comp. Probs. in Abstract Algebra 329-358 (Pergamon Press, 1970)