K12a1249

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1249

Polynomial invariants

Jones polynomial	$q^{6}-5q^{5}+12q^{4}-21q^{3}+31q^{2}-38q+41-38q^{-1}+31q^{-2}-21q^{-3}+12q^{-4}-5q^{-5}+q^{-6}$
Alexander polynomial	$-t^{5}+6t^{4}-17t^{3}+32t^{2}-46t+53-46t^{-1}+32t^{-2}-17t^{-3}+6t^{-4}-t^{-5}$
Conway polynomial	$-z^{10}-4z^{8}-4z^{6}+1$
Determinant	257
Signature	0
HOMFLY-PT polynomial	$-z^{10}+a^{2}z^{8}+z^{8}a^{-2}-6z^{8}+4a^{2}z^{6}+4z^{6}a^{-2}-12z^{6}+4a^{2}z^{4}+4z^{4}a^{-2}-8z^{4}+1$
Kauffman polynomial	$4az^{11}+4z^{11}a^{-1}+11a^{2}z^{10}+11z^{10}a^{-2}+22z^{10}+14a^{3}z^{9}+18az^{9}+18z^{9}a^{-1}+14z^{9}a^{-3}+11a^{4}z^{8}-10a^{2}z^{8}-10z^{8}a^{-2}+11z^{8}a^{-4}-42z^{8}+5a^{5}z^{7}-25a^{3}z^{7}-55az^{7}-55z^{7}a^{-1}-25z^{7}a^{-3}+5z^{7}a^{-5}+a^{6}z^{6}-21a^{4}z^{6}-11a^{2}z^{6}-11z^{6}a^{-2}-21z^{6}a^{-4}+z^{6}a^{-6}+22z^{6}-8a^{5}z^{5}+11a^{3}z^{5}+48az^{5}+48z^{5}a^{-1}+11z^{5}a^{-3}-8z^{5}a^{-5}-a^{6}z^{4}+10a^{4}z^{4}+14a^{2}z^{4}+14z^{4}a^{-2}+10z^{4}a^{-4}-z^{4}a^{-6}+6z^{4}+2a^{5}z^{3}-a^{3}z^{3}-13az^{3}-13z^{3}a^{-1}-z^{3}a^{-3}+2z^{3}a^{-5}-a^{4}z^{2}-4a^{2}z^{2}-4z^{2}a^{-2}-z^{2}a^{-4}-6z^{2}+1$

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