K13a1424

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a1424

Polynomial invariants

Jones polynomial	Data:K13a1424/Jones Polynomial
Alexander polynomial	$t^{4}-11t^{3}+48t^{2}-109t+143-109t^{-1}+48t^{-2}-11t^{-3}+t^{-4}$
Conway polynomial	Data:K13a1424/Conway Polynomial
Determinant	481
Signature	0
HOMFLY-PT polynomial	$z^{8}-3a^{2}z^{6}-2z^{6}a^{-2}+2z^{6}+3a^{4}z^{4}-4a^{2}z^{4}-2z^{4}a^{-2}+z^{4}a^{-4}+4z^{4}-a^{6}z^{2}+2a^{4}z^{2}-2a^{2}z^{2}-z^{2}a^{-2}+2z^{2}+1$
Kauffman polynomial	$5a^{2}z^{12}+5z^{12}+14a^{3}z^{11}+33az^{11}+19z^{11}a^{-1}+17a^{4}z^{10}+36a^{2}z^{10}+31z^{10}a^{-2}+50z^{10}+12a^{5}z^{9}-5a^{3}z^{9}-39az^{9}+7z^{9}a^{-1}+29z^{9}a^{-3}+5a^{6}z^{8}-32a^{4}z^{8}-104a^{2}z^{8}-44z^{8}a^{-2}+17z^{8}a^{-4}-128z^{8}+a^{7}z^{7}-27a^{5}z^{7}-42a^{3}z^{7}-35az^{7}-73z^{7}a^{-1}-46z^{7}a^{-3}+6z^{7}a^{-5}-11a^{6}z^{6}+16a^{4}z^{6}+87a^{2}z^{6}+11z^{6}a^{-2}-21z^{6}a^{-4}+z^{6}a^{-6}+93z^{6}-2a^{7}z^{5}+22a^{5}z^{5}+51a^{3}z^{5}+60az^{5}+59z^{5}a^{-1}+22z^{5}a^{-3}-4z^{5}a^{-5}+8a^{6}z^{4}-28a^{2}z^{4}+3z^{4}a^{-2}+6z^{4}a^{-4}-23z^{4}+a^{7}z^{3}-8a^{5}z^{3}-22a^{3}z^{3}-24az^{3}-14z^{3}a^{-1}-3z^{3}a^{-3}-2a^{6}z^{2}-a^{4}z^{2}+3a^{2}z^{2}-z^{2}a^{-2}+z^{2}+a^{5}z+3a^{3}z+3az+za^{-1}+1$

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