K12n714

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12n714

Polynomial invariants

Jones polynomial	$-q^{8}+4q^{7}-9q^{6}+15q^{5}-20q^{4}+22q^{3}-21q^{2}+18q-12+7q^{-1}-2q^{-2}$
Alexander polynomial	$3t^{3}-14t^{2}+30t-37+30t^{-1}-14t^{-2}+3t^{-3}$
Conway polynomial	$3z^{6}+4z^{4}+z^{2}+1$
Determinant	131
Signature	2
HOMFLY-PT polynomial	$2z^{6}a^{-2}+z^{6}a^{-4}+6z^{4}a^{-2}+z^{4}a^{-4}-z^{4}a^{-6}-2z^{4}+6z^{2}a^{-2}-z^{2}a^{-4}-z^{2}a^{-6}-3z^{2}+2a^{-2}-a^{-4}$
Kauffman polynomial	$2z^{10}a^{-2}+2z^{10}a^{-4}+3z^{9}a^{-1}+10z^{9}a^{-3}+7z^{9}a^{-5}+3z^{8}a^{-2}+12z^{8}a^{-4}+10z^{8}a^{-6}+z^{8}-z^{7}a^{-1}-13z^{7}a^{-3}-4z^{7}a^{-5}+8z^{7}a^{-7}-26z^{6}a^{-4}-16z^{6}a^{-6}+4z^{6}a^{-8}+6z^{6}+3az^{5}+3z^{5}a^{-3}-7z^{5}a^{-5}-12z^{5}a^{-7}+z^{5}a^{-9}-16z^{4}a^{-2}+13z^{4}a^{-4}+10z^{4}a^{-6}-5z^{4}a^{-8}-14z^{4}-4az^{3}-6z^{3}a^{-1}-2z^{3}a^{-3}+7z^{3}a^{-5}+6z^{3}a^{-7}-z^{3}a^{-9}+11z^{2}a^{-2}+z^{2}a^{-4}-2z^{2}a^{-6}+z^{2}a^{-8}+7z^{2}+az+2za^{-1}+za^{-3}-za^{-5}-za^{-7}-2a^{-2}-a^{-4}$

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