K12a1

Knot presentations

Dowker-Thistlethwaite code

4 8 10 14 2 16 20 6 22 12 24 18

Notes on presentations of K12a1

Polynomial invariants

Jones polynomial	$-q^{5}+4q^{4}-10q^{3}+19q^{2}-26q+32-34q^{-1}+31q^{-2}-25q^{-3}+17q^{-4}-9q^{-5}+4q^{-6}-q^{-7}$
Alexander polynomial	$t^{4}-7t^{3}+23t^{2}-46t+59-46t^{-1}+23t^{-2}-7t^{-3}+t^{-4}$
Conway polynomial	$z^{8}+z^{6}+z^{4}-z^{2}+1$
Determinant	213
Signature	0
HOMFLY-PT polynomial	$z^{8}-3a^{2}z^{6}-z^{6}a^{-2}+5z^{6}+3a^{4}z^{4}-11a^{2}z^{4}-3z^{4}a^{-2}+12z^{4}-a^{6}z^{2}+7a^{4}z^{2}-16a^{2}z^{2}-4z^{2}a^{-2}+13z^{2}-a^{6}+5a^{4}-8a^{2}-a^{-2}+6$
Kauffman polynomial	$a^{3}z^{11}+az^{11}+4a^{4}z^{10}+10a^{2}z^{10}+6z^{10}+6a^{5}z^{9}+20a^{3}z^{9}+27az^{9}+13z^{9}a^{-1}+4a^{6}z^{8}+7a^{4}z^{8}+8a^{2}z^{8}+14z^{8}a^{-2}+19z^{8}+a^{7}z^{7}-14a^{5}z^{7}-56a^{3}z^{7}-64az^{7}-14z^{7}a^{-1}+9z^{7}a^{-3}-13a^{6}z^{6}-49a^{4}z^{6}-81a^{2}z^{6}-23z^{6}a^{-2}+4z^{6}a^{-4}-72z^{6}-3a^{7}z^{5}+6a^{5}z^{5}+41a^{3}z^{5}+44az^{5}-11z^{5}a^{-3}+z^{5}a^{-5}+15a^{6}z^{4}+62a^{4}z^{4}+101a^{2}z^{4}+21z^{4}a^{-2}-4z^{4}a^{-4}+79z^{4}+3a^{7}z^{3}+4a^{5}z^{3}-9a^{3}z^{3}-12az^{3}+5z^{3}a^{-1}+6z^{3}a^{-3}-z^{3}a^{-5}-7a^{6}z^{2}-30a^{4}z^{2}-50a^{2}z^{2}-10z^{2}a^{-2}+z^{2}a^{-4}-38z^{2}-a^{7}z-2a^{5}z+a^{3}z+2az-za^{-1}-za^{-3}+a^{6}+5a^{4}+8a^{2}+a^{-2}+6$

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