K13a2613

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a2613

Polynomial invariants

Jones polynomial	Data:K13a2613/Jones Polynomial
Alexander polynomial	$t^{5}-5t^{4}+15t^{3}-30t^{2}+45t-51+45t^{-1}-30t^{-2}+15t^{-3}-5t^{-4}+t^{-5}$
Conway polynomial	Data:K13a2613/Conway Polynomial
Determinant	243
Signature	2
HOMFLY-PT polynomial	$z^{10}a^{-2}+8z^{8}a^{-2}-2z^{8}a^{-4}-z^{8}+28z^{6}a^{-2}-13z^{6}a^{-4}+z^{6}a^{-6}-6z^{6}+53z^{4}a^{-2}-33z^{4}a^{-4}+5z^{4}a^{-6}-15z^{4}+53z^{2}a^{-2}-38z^{2}a^{-4}+8z^{2}a^{-6}-18z^{2}+22a^{-2}-17a^{-4}+4a^{-6}-8$
Kauffman polynomial	$z^{12}a^{-2}+z^{12}a^{-4}+4z^{11}a^{-1}+8z^{11}a^{-3}+4z^{11}a^{-5}+15z^{10}a^{-2}+15z^{10}a^{-4}+7z^{10}a^{-6}+7z^{10}+6az^{9}+4z^{9}a^{-1}-4z^{9}a^{-3}+5z^{9}a^{-5}+7z^{9}a^{-7}+3a^{2}z^{8}-54z^{8}a^{-2}-51z^{8}a^{-4}-13z^{8}a^{-6}+5z^{8}a^{-8}-18z^{8}+a^{3}z^{7}-18az^{7}-42z^{7}a^{-1}-44z^{7}a^{-3}-39z^{7}a^{-5}-15z^{7}a^{-7}+3z^{7}a^{-9}-9a^{2}z^{6}+86z^{6}a^{-2}+80z^{6}a^{-4}+12z^{6}a^{-6}-10z^{6}a^{-8}+z^{6}a^{-10}+20z^{6}-4a^{3}z^{5}+19az^{5}+75z^{5}a^{-1}+109z^{5}a^{-3}+79z^{5}a^{-5}+14z^{5}a^{-7}-8z^{5}a^{-9}+7a^{2}z^{4}-92z^{4}a^{-2}-70z^{4}a^{-4}-5z^{4}a^{-6}+4z^{4}a^{-8}-3z^{4}a^{-10}-27z^{4}+5a^{3}z^{3}-13az^{3}-71z^{3}a^{-1}-106z^{3}a^{-3}-66z^{3}a^{-5}-7z^{3}a^{-7}+6z^{3}a^{-9}-a^{2}z^{2}+62z^{2}a^{-2}+46z^{2}a^{-4}+6z^{2}a^{-6}+2z^{2}a^{-10}+23z^{2}-2a^{3}z+5az+26za^{-1}+39za^{-3}+23za^{-5}+za^{-7}-2za^{-9}-22a^{-2}-17a^{-4}-4a^{-6}-8$

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