K13a742

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a742

Polynomial invariants

Jones polynomial	Data:K13a742/Jones Polynomial
Alexander polynomial	$2t^{4}-10t^{3}+26t^{2}-43t+51-43t^{-1}+26t^{-2}-10t^{-3}+2t^{-4}$
Conway polynomial	Data:K13a742/Conway Polynomial
Determinant	213
Signature	0
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}-a^{2}z^{6}+4z^{6}a^{-2}-2z^{6}a^{-4}+5z^{6}-4a^{2}z^{4}+6z^{4}a^{-2}-7z^{4}a^{-4}+z^{4}a^{-6}+10z^{4}-5a^{2}z^{2}+5z^{2}a^{-2}-8z^{2}a^{-4}+2z^{2}a^{-6}+9z^{2}-2a^{2}+3a^{-2}-4a^{-4}+a^{-6}+3$
Kauffman polynomial	$z^{12}a^{-2}+z^{12}a^{-4}+4z^{11}a^{-1}+8z^{11}a^{-3}+4z^{11}a^{-5}+14z^{10}a^{-2}+13z^{10}a^{-4}+6z^{10}a^{-6}+7z^{10}+8az^{9}+4z^{9}a^{-1}-11z^{9}a^{-3}-3z^{9}a^{-5}+4z^{9}a^{-7}+7a^{2}z^{8}-52z^{8}a^{-2}-59z^{8}a^{-4}-22z^{8}a^{-6}+z^{8}a^{-8}-9z^{8}+5a^{3}z^{7}-13az^{7}-36z^{7}a^{-1}-37z^{7}a^{-3}-36z^{7}a^{-5}-17z^{7}a^{-7}+3a^{4}z^{6}-10a^{2}z^{6}+56z^{6}a^{-2}+71z^{6}a^{-4}+20z^{6}a^{-6}-4z^{6}a^{-8}-4z^{6}+a^{5}z^{5}-6a^{3}z^{5}+10az^{5}+49z^{5}a^{-1}+76z^{5}a^{-3}+67z^{5}a^{-5}+23z^{5}a^{-7}-5a^{4}z^{4}+8a^{2}z^{4}-24z^{4}a^{-2}-36z^{4}a^{-4}-3z^{4}a^{-6}+5z^{4}a^{-8}+17z^{4}-2a^{5}z^{3}+a^{3}z^{3}-2az^{3}-24z^{3}a^{-1}-49z^{3}a^{-3}-43z^{3}a^{-5}-13z^{3}a^{-7}+2a^{4}z^{2}-6a^{2}z^{2}+6z^{2}a^{-2}+12z^{2}a^{-4}-2z^{2}a^{-8}-12z^{2}+a^{5}z-az+4za^{-1}+12za^{-3}+11za^{-5}+3za^{-7}+2a^{2}-3a^{-2}-4a^{-4}-a^{-6}+3$

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