K13a4540

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4540

Polynomial invariants

Jones polynomial	Data:K13a4540/Jones Polynomial
Alexander polynomial	$-4t^{3}+22t^{2}-44t+53-44t^{-1}+22t^{-2}-4t^{-3}$
Conway polynomial	Data:K13a4540/Conway Polynomial
Determinant	193
Signature	-4
HOMFLY-PT polynomial	$-z^{2}a^{12}-a^{12}+2z^{4}a^{10}+3z^{2}a^{10}-z^{6}a^{8}+3z^{2}a^{8}+a^{8}-2z^{6}a^{6}-4z^{4}a^{6}-z^{2}a^{6}-z^{6}a^{4}-z^{4}a^{4}+2z^{2}a^{4}+a^{4}+z^{4}a^{2}+2z^{2}a^{2}$
Kauffman polynomial	$z^{7}a^{15}-4z^{5}a^{15}+4z^{3}a^{15}-za^{15}+3z^{8}a^{14}-11z^{6}a^{14}+10z^{4}a^{14}-2z^{2}a^{14}+5z^{9}a^{13}-18z^{7}a^{13}+20z^{5}a^{13}-11z^{3}a^{13}+3za^{13}+5z^{10}a^{12}-15z^{8}a^{12}+14z^{6}a^{12}-8z^{4}a^{12}+3z^{2}a^{12}-a^{12}+3z^{11}a^{11}-3z^{9}a^{11}-9z^{7}a^{11}+15z^{5}a^{11}-7z^{3}a^{11}-za^{11}+z^{12}a^{10}+5z^{10}a^{10}-19z^{8}a^{10}+25z^{6}a^{10}-15z^{4}a^{10}+3z^{2}a^{10}+6z^{11}a^{9}-16z^{9}a^{9}+28z^{7}a^{9}-33z^{5}a^{9}+25z^{3}a^{9}-7za^{9}+z^{12}a^{8}+5z^{10}a^{8}-15z^{8}a^{8}+23z^{6}a^{8}-16z^{4}a^{8}+5z^{2}a^{8}+a^{8}+3z^{11}a^{7}-2z^{9}a^{7}+z^{7}a^{7}-z^{5}a^{7}+3z^{3}a^{7}-2za^{7}+5z^{10}a^{6}-9z^{8}a^{6}+10z^{6}a^{6}-7z^{4}a^{6}+z^{2}a^{6}+6z^{9}a^{5}-14z^{7}a^{5}+15z^{5}a^{5}-9z^{3}a^{5}+5z^{8}a^{4}-12z^{6}a^{4}+9z^{4}a^{4}-4z^{2}a^{4}+a^{4}+3z^{7}a^{3}-8z^{5}a^{3}+5z^{3}a^{3}+z^{6}a^{2}-3z^{4}a^{2}+2z^{2}a^{2}$

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