K12a1146

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1146

Polynomial invariants

Jones polynomial	$q^{8}-2q^{7}+5q^{6}-9q^{5}+12q^{4}-16q^{3}+18q^{2}-17q+15-11q^{-1}+7q^{-2}-3q^{-3}+q^{-4}$
Alexander polynomial	$-4t^{3}+14t^{2}-25t+31-25t^{-1}+14t^{-2}-4t^{-3}$
Conway polynomial	$-4z^{6}-10z^{4}-5z^{2}+1$
Determinant	117
Signature	0
HOMFLY-PT polynomial	$-2z^{6}a^{-2}-z^{6}a^{-4}-z^{6}+a^{2}z^{4}-7z^{4}a^{-2}-3z^{4}a^{-4}+z^{4}a^{-6}-2z^{4}+2a^{2}z^{2}-7z^{2}a^{-2}-3z^{2}a^{-4}+3z^{2}a^{-6}+a^{2}-a^{-2}-2a^{-4}+2a^{-6}+1$
Kauffman polynomial	$z^{11}a^{-3}+z^{11}a^{-5}+3z^{10}a^{-2}+5z^{10}a^{-4}+2z^{10}a^{-6}+6z^{9}a^{-1}+4z^{9}a^{-3}+2z^{9}a^{-7}+z^{8}a^{-2}-15z^{8}a^{-4}-7z^{8}a^{-6}+z^{8}a^{-8}+8z^{8}+8az^{7}-8z^{7}a^{-1}-13z^{7}a^{-3}-7z^{7}a^{-5}-10z^{7}a^{-7}+6a^{2}z^{6}-15z^{6}a^{-2}+14z^{6}a^{-4}+5z^{6}a^{-6}-6z^{6}a^{-8}-12z^{6}+3a^{3}z^{5}-11az^{5}+2z^{5}a^{-1}+z^{5}a^{-3}+z^{5}a^{-5}+16z^{5}a^{-7}+a^{4}z^{4}-7a^{2}z^{4}+13z^{4}a^{-2}-14z^{4}a^{-4}+12z^{4}a^{-8}+7z^{4}-2a^{3}z^{3}+7az^{3}-3z^{3}a^{-1}+6z^{3}a^{-3}+9z^{3}a^{-5}-9z^{3}a^{-7}-a^{4}z^{2}+5a^{2}z^{2}-9z^{2}a^{-2}+11z^{2}a^{-4}+4z^{2}a^{-6}-8z^{2}a^{-8}-2z^{2}-3za^{-3}-za^{-5}+2za^{-7}-a^{2}+a^{-2}-2a^{-4}-2a^{-6}+1$

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