K12a48

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a48

Polynomial invariants

Jones polynomial	$q^{6}-5q^{5}+12q^{4}-22q^{3}+33q^{2}-39q+42-39q^{-1}+31q^{-2}-21q^{-3}+11q^{-4}-4q^{-5}+q^{-6}$
Alexander polynomial	$t^{4}-8t^{3}+28t^{2}-57t+73-57t^{-1}+28t^{-2}-8t^{-3}+t^{-4}$
Conway polynomial	$z^{8}-z^{2}+1$
Determinant	261
Signature	0
HOMFLY-PT polynomial	$z^{8}-2a^{2}z^{6}-2z^{6}a^{-2}+4z^{6}+a^{4}z^{4}-6a^{2}z^{4}-5z^{4}a^{-2}+z^{4}a^{-4}+9z^{4}+2a^{4}z^{2}-9a^{2}z^{2}-5z^{2}a^{-2}+z^{2}a^{-4}+10z^{2}+2a^{4}-5a^{2}-a^{-2}+5$
Kauffman polynomial	$2az^{11}+2z^{11}a^{-1}+8a^{2}z^{10}+8z^{10}a^{-2}+16z^{10}+12a^{3}z^{9}+30az^{9}+31z^{9}a^{-1}+13z^{9}a^{-3}+9a^{4}z^{8}+9a^{2}z^{8}+15z^{8}a^{-2}+11z^{8}a^{-4}+4z^{8}+4a^{5}z^{7}-19a^{3}z^{7}-70az^{7}-67z^{7}a^{-1}-15z^{7}a^{-3}+5z^{7}a^{-5}+a^{6}z^{6}-17a^{4}z^{6}-50a^{2}z^{6}-63z^{6}a^{-2}-20z^{6}a^{-4}+z^{6}a^{-6}-74z^{6}-7a^{5}z^{5}+12a^{3}z^{5}+53az^{5}+38z^{5}a^{-1}-4z^{5}a^{-3}-8z^{5}a^{-5}-2a^{6}z^{4}+15a^{4}z^{4}+58a^{2}z^{4}+57z^{4}a^{-2}+14z^{4}a^{-4}-z^{4}a^{-6}+83z^{4}+4a^{5}z^{3}-4a^{3}z^{3}-19az^{3}-8z^{3}a^{-1}+7z^{3}a^{-3}+4z^{3}a^{-5}+a^{6}z^{2}-8a^{4}z^{2}-29a^{2}z^{2}-20z^{2}a^{-2}-4z^{2}a^{-4}-36z^{2}-a^{5}z+a^{3}z+4az+2za^{-1}+2a^{4}+5a^{2}+a^{-2}+5$

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