K13a4130

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4130

Polynomial invariants

Jones polynomial	Data:K13a4130/Jones Polynomial
Alexander polynomial	$t^{5}-7t^{4}+23t^{3}-50t^{2}+78t-89+78t^{-1}-50t^{-2}+23t^{-3}-7t^{-4}+t^{-5}$
Conway polynomial	Data:K13a4130/Conway Polynomial
Determinant	407
Signature	2
HOMFLY-PT polynomial	$z^{10}a^{-2}+6z^{8}a^{-2}-z^{8}a^{-4}-2z^{8}+a^{2}z^{6}+14z^{6}a^{-2}-4z^{6}a^{-4}-9z^{6}+3a^{2}z^{4}+14z^{4}a^{-2}-5z^{4}a^{-4}-14z^{4}+3a^{2}z^{2}+4z^{2}a^{-2}-z^{2}a^{-4}-8z^{2}+a^{2}-a^{-2}+a^{-4}$
Kauffman polynomial	$5z^{12}a^{-2}+5z^{12}+12az^{11}+31z^{11}a^{-1}+19z^{11}a^{-3}+11a^{2}z^{10}+42z^{10}a^{-2}+32z^{10}a^{-4}+21z^{10}+5a^{3}z^{9}-26az^{9}-70z^{9}a^{-1}-6z^{9}a^{-3}+33z^{9}a^{-5}+a^{4}z^{8}-35a^{2}z^{8}-155z^{8}a^{-2}-58z^{8}a^{-4}+24z^{8}a^{-6}-109z^{8}-16a^{3}z^{7}-4az^{7}+4z^{7}a^{-1}-80z^{7}a^{-3}-59z^{7}a^{-5}+13z^{7}a^{-7}-3a^{4}z^{6}+36a^{2}z^{6}+151z^{6}a^{-2}+24z^{6}a^{-4}-31z^{6}a^{-6}+5z^{6}a^{-8}+130z^{6}+17a^{3}z^{5}+31az^{5}+63z^{5}a^{-1}+98z^{5}a^{-3}+38z^{5}a^{-5}-10z^{5}a^{-7}+z^{5}a^{-9}+3a^{4}z^{4}-17a^{2}z^{4}-48z^{4}a^{-2}+6z^{4}a^{-4}+12z^{4}a^{-6}-2z^{4}a^{-8}-60z^{4}-7a^{3}z^{3}-18az^{3}-36z^{3}a^{-1}-36z^{3}a^{-3}-10z^{3}a^{-5}+z^{3}a^{-7}-a^{4}z^{2}+5a^{2}z^{2}+z^{2}a^{-2}-5z^{2}a^{-4}-z^{2}a^{-6}+11z^{2}+a^{3}z+3az+5za^{-1}+3za^{-3}-a^{2}+a^{-2}+a^{-4}$

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