K12a1001

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1001

Polynomial invariants

Jones polynomial	$q^{8}-4q^{7}+9q^{6}-15q^{5}+22q^{4}-27q^{3}+29q^{2}-28q+23-16q^{-1}+10q^{-2}-4q^{-3}+q^{-4}$
Alexander polynomial	$-4t^{3}+19t^{2}-43t+57-43t^{-1}+19t^{-2}-4t^{-3}$
Conway polynomial	$-4z^{6}-5z^{4}-3z^{2}+1$
Determinant	189
Signature	0
HOMFLY-PT polynomial	$-2z^{6}a^{-2}-z^{6}a^{-4}-z^{6}+a^{2}z^{4}-5z^{4}a^{-2}-z^{4}a^{-4}+z^{4}a^{-6}-z^{4}+a^{2}z^{2}-6z^{2}a^{-2}+z^{2}a^{-4}+z^{2}a^{-6}+a^{2}-3a^{-2}+2a^{-4}+1$
Kauffman polynomial	$3z^{11}a^{-3}+3z^{11}a^{-5}+10z^{10}a^{-2}+16z^{10}a^{-4}+6z^{10}a^{-6}+17z^{9}a^{-1}+15z^{9}a^{-3}+2z^{9}a^{-5}+4z^{9}a^{-7}-8z^{8}a^{-2}-51z^{8}a^{-4}-23z^{8}a^{-6}+z^{8}a^{-8}+19z^{8}+16az^{7}-31z^{7}a^{-1}-70z^{7}a^{-3}-40z^{7}a^{-5}-17z^{7}a^{-7}+10a^{2}z^{6}-33z^{6}a^{-2}+37z^{6}a^{-4}+25z^{6}a^{-6}-4z^{6}a^{-8}-31z^{6}+4a^{3}z^{5}-20az^{5}+12z^{5}a^{-1}+71z^{5}a^{-3}+58z^{5}a^{-5}+23z^{5}a^{-7}+a^{4}z^{4}-8a^{2}z^{4}+40z^{4}a^{-2}+7z^{4}a^{-4}-6z^{4}a^{-6}+5z^{4}a^{-8}+13z^{4}+7az^{3}-7z^{3}a^{-1}-25z^{3}a^{-3}-22z^{3}a^{-5}-11z^{3}a^{-7}+4a^{2}z^{2}-19z^{2}a^{-2}-10z^{2}a^{-4}-z^{2}a^{-6}-2z^{2}a^{-8}-4z^{2}+3za^{-1}+4za^{-3}+2za^{-5}+za^{-7}-a^{2}+3a^{-2}+2a^{-4}+1$

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