K12a954

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a954

Polynomial invariants

Jones polynomial	$q^{9}-4q^{8}+9q^{7}-17q^{6}+25q^{5}-31q^{4}+34q^{3}-31q^{2}+26q-18+10q^{-1}-4q^{-2}+q^{-3}$
Alexander polynomial	$-2t^{4}+10t^{3}-25t^{2}+43t-51+43t^{-1}-25t^{-2}+10t^{-3}-2t^{-4}$
Conway polynomial	$-2z^{8}-6z^{6}-5z^{4}+z^{2}+1$
Determinant	211
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}a^{-4}-4z^{6}a^{-2}-4z^{6}a^{-4}+z^{6}a^{-6}+z^{6}-6z^{4}a^{-2}-5z^{4}a^{-4}+3z^{4}a^{-6}+3z^{4}-4z^{2}a^{-2}+2z^{2}a^{-6}+3z^{2}-a^{-2}+2a^{-4}-a^{-6}+1$
Kauffman polynomial	$3z^{11}a^{-3}+3z^{11}a^{-5}+9z^{10}a^{-2}+16z^{10}a^{-4}+7z^{10}a^{-6}+12z^{9}a^{-1}+12z^{9}a^{-3}+8z^{9}a^{-5}+8z^{9}a^{-7}-15z^{8}a^{-2}-39z^{8}a^{-4}-8z^{8}a^{-6}+7z^{8}a^{-8}+9z^{8}+4az^{7}-31z^{7}a^{-1}-45z^{7}a^{-3}-24z^{7}a^{-5}-10z^{7}a^{-7}+4z^{7}a^{-9}+a^{2}z^{6}+4z^{6}a^{-2}+46z^{6}a^{-4}+5z^{6}a^{-6}-13z^{6}a^{-8}+z^{6}a^{-10}-22z^{6}-8az^{5}+31z^{5}a^{-1}+56z^{5}a^{-3}+22z^{5}a^{-5}-4z^{5}a^{-7}-9z^{5}a^{-9}-2a^{2}z^{4}+9z^{4}a^{-2}-26z^{4}a^{-4}-9z^{4}a^{-6}+5z^{4}a^{-8}-2z^{4}a^{-10}+17z^{4}+2az^{3}-14z^{3}a^{-1}-27z^{3}a^{-3}-9z^{3}a^{-5}+8z^{3}a^{-7}+6z^{3}a^{-9}-6z^{2}a^{-2}+3z^{2}a^{-4}+3z^{2}a^{-6}+z^{2}a^{-8}+z^{2}a^{-10}-6z^{2}+2za^{-1}+4za^{-3}-3za^{-7}-za^{-9}+a^{-2}+2a^{-4}+a^{-6}+1$

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