K12a1065

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1065

Polynomial invariants

Jones polynomial	$-q^{7}+5q^{6}-13q^{5}+24q^{4}-36q^{3}+45q^{2}-48q+46-37q^{-1}+26q^{-2}-14q^{-3}+5q^{-4}-q^{-5}$
Alexander polynomial	$t^{4}-8t^{3}+31t^{2}-67t+87-67t^{-1}+31t^{-2}-8t^{-3}+t^{-4}$
Conway polynomial	$z^{8}+3z^{4}+z^{2}+1$
Determinant	301
Signature	0
HOMFLY-PT polynomial	$z^{8}-a^{2}z^{6}-3z^{6}a^{-2}+4z^{6}-2a^{2}z^{4}-7z^{4}a^{-2}+3z^{4}a^{-4}+9z^{4}-3a^{2}z^{2}-6z^{2}a^{-2}+3z^{2}a^{-4}-z^{2}a^{-6}+8z^{2}-a^{2}-a^{-2}+3$
Kauffman polynomial	$5z^{11}a^{-1}+5z^{11}a^{-3}+30z^{10}a^{-2}+12z^{10}a^{-4}+18z^{10}+28az^{9}+39z^{9}a^{-1}+22z^{9}a^{-3}+11z^{9}a^{-5}+25a^{2}z^{8}-53z^{8}a^{-2}-20z^{8}a^{-4}+5z^{8}a^{-6}-3z^{8}+14a^{3}z^{7}-42az^{7}-111z^{7}a^{-1}-84z^{7}a^{-3}-28z^{7}a^{-5}+z^{7}a^{-7}+5a^{4}z^{6}-36a^{2}z^{6}+z^{6}a^{-2}-3z^{6}a^{-4}-12z^{6}a^{-6}-49z^{6}+a^{5}z^{5}-12a^{3}z^{5}+18az^{5}+82z^{5}a^{-1}+77z^{5}a^{-3}+24z^{5}a^{-5}-2z^{5}a^{-7}-a^{4}z^{4}+22a^{2}z^{4}+25z^{4}a^{-2}+15z^{4}a^{-4}+9z^{4}a^{-6}+42z^{4}+5a^{3}z^{3}-2az^{3}-22z^{3}a^{-1}-24z^{3}a^{-3}-8z^{3}a^{-5}+z^{3}a^{-7}-7a^{2}z^{2}-9z^{2}a^{-2}-4z^{2}a^{-4}-2z^{2}a^{-6}-14z^{2}-a^{3}z-az+za^{-1}+2za^{-3}+za^{-5}+a^{2}+a^{-2}+3$

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