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I want to point out that although the Alexander-Conway polynomial cannot distinguish a knot from its mirror image, it can detect certain kinds of chirality. In fact, I made a conjecture many years ago that I wish someone would solve. Any amphicheiral knot has conway polynomial that splits as $f(z)f(-z)$ with coefficients taken modulo $4$. See arxiv.org/pdf/1608.04453.pdf