K13a2719

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a2719

Polynomial invariants

Jones polynomial	Data:K13a2719/Jones Polynomial
Alexander polynomial	$3t^{3}-17t^{2}+45t-61+45t^{-1}-17t^{-2}+3t^{-3}$
Conway polynomial	Data:K13a2719/Conway Polynomial
Determinant	191
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+z^{6}a^{-4}+z^{6}a^{-6}+2z^{4}a^{-2}+2z^{4}a^{-6}-2z^{4}a^{-8}-z^{4}+3z^{2}a^{-2}-z^{2}a^{-4}+5z^{2}a^{-6}-3z^{2}a^{-8}+z^{2}a^{-10}-z^{2}+a^{-2}-a^{-4}+3a^{-6}-2a^{-8}$
Kauffman polynomial	$z^{12}a^{-6}+z^{12}a^{-8}+4z^{11}a^{-5}+8z^{11}a^{-7}+4z^{11}a^{-9}+7z^{10}a^{-4}+12z^{10}a^{-6}+11z^{10}a^{-8}+6z^{10}a^{-10}+8z^{9}a^{-3}-z^{9}a^{-5}-22z^{9}a^{-7}-9z^{9}a^{-9}+4z^{9}a^{-11}+8z^{8}a^{-2}-13z^{8}a^{-4}-58z^{8}a^{-6}-66z^{8}a^{-8}-28z^{8}a^{-10}+z^{8}a^{-12}+7z^{7}a^{-1}-10z^{7}a^{-3}-22z^{7}a^{-5}-5z^{7}a^{-7}-19z^{7}a^{-9}-19z^{7}a^{-11}-8z^{6}a^{-2}+14z^{6}a^{-4}+93z^{6}a^{-6}+110z^{6}a^{-8}+39z^{6}a^{-10}-4z^{6}a^{-12}+4z^{6}+az^{5}-10z^{5}a^{-1}+2z^{5}a^{-3}+40z^{5}a^{-5}+55z^{5}a^{-7}+53z^{5}a^{-9}+25z^{5}a^{-11}-4z^{4}a^{-2}-14z^{4}a^{-4}-68z^{4}a^{-6}-77z^{4}a^{-8}-22z^{4}a^{-10}+3z^{4}a^{-12}-6z^{4}-az^{3}+3z^{3}a^{-1}-26z^{3}a^{-5}-48z^{3}a^{-7}-36z^{3}a^{-9}-10z^{3}a^{-11}+5z^{2}a^{-2}+8z^{2}a^{-4}+23z^{2}a^{-6}+23z^{2}a^{-8}+5z^{2}a^{-10}+2z^{2}+za^{-3}+5za^{-5}+11za^{-7}+7za^{-9}-a^{-2}-a^{-4}-3a^{-6}-2a^{-8}$

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