K13a4676

Knot presentations

Dowker-Thistlethwaite code

6 20 18 16 24 4 2 22 26 12 14 8 10

Notes on presentations of K13a4676

Polynomial invariants

Jones polynomial	Data:K13a4676/Jones Polynomial
Alexander polynomial	$t^{5}-7t^{4}+22t^{3}-45t^{2}+67t-75+67t^{-1}-45t^{-2}+22t^{-3}-7t^{-4}+t^{-5}$
Conway polynomial	Data:K13a4676/Conway Polynomial
Determinant	359
Signature	-2
HOMFLY-PT polynomial	$a^{2}z^{10}-a^{4}z^{8}+6a^{2}z^{8}-2z^{8}-4a^{4}z^{6}+13a^{2}z^{6}+z^{6}a^{-2}-9z^{6}-4a^{4}z^{4}+10a^{2}z^{4}+3z^{4}a^{-2}-12z^{4}+a^{4}z^{2}-2a^{2}z^{2}+2z^{2}a^{-2}-3z^{2}+2a^{4}-4a^{2}+3$
Kauffman polynomial	$5a^{2}z^{12}+5z^{12}+16a^{3}z^{11}+28az^{11}+12z^{11}a^{-1}+25a^{4}z^{10}+26a^{2}z^{10}+11z^{10}a^{-2}+12z^{10}+26a^{5}z^{9}-15a^{3}z^{9}-82az^{9}-36z^{9}a^{-1}+5z^{9}a^{-3}+20a^{6}z^{8}-47a^{4}z^{8}-115a^{2}z^{8}-40z^{8}a^{-2}+z^{8}a^{-4}-89z^{8}+12a^{7}z^{7}-45a^{5}z^{7}-39a^{3}z^{7}+60az^{7}+25z^{7}a^{-1}-17z^{7}a^{-3}+5a^{8}z^{6}-25a^{6}z^{6}+23a^{4}z^{6}+125a^{2}z^{6}+46z^{6}a^{-2}-3z^{6}a^{-4}+121z^{6}+a^{9}z^{5}-11a^{7}z^{5}+24a^{5}z^{5}+54a^{3}z^{5}+2az^{5}+16z^{5}a^{-3}-3a^{8}z^{4}+5a^{6}z^{4}+a^{4}z^{4}-41a^{2}z^{4}-23z^{4}a^{-2}+2z^{4}a^{-4}-59z^{4}+a^{7}z^{3}-2a^{5}z^{3}-14a^{3}z^{3}-10az^{3}-3z^{3}a^{-1}-4z^{3}a^{-3}+2a^{6}z^{2}-3a^{4}z^{2}-5a^{2}z^{2}+5z^{2}a^{-2}+5z^{2}-2a^{5}z-2a^{3}z+2a^{4}+4a^{2}+3$

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