K12a561

Knotscape

Three-fold symmetrical depiction as decorative knot

Inside triangle

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a561

Polynomial invariants

Jones polynomial	$-q^{11}+5q^{10}-12q^{9}+20q^{8}-29q^{7}+34q^{6}-35q^{5}+33q^{4}-25q^{3}+17q^{2}-9q+4-q^{-1}$
Alexander polynomial	$t^{4}-7t^{3}+25t^{2}-49t+61-49t^{-1}+25t^{-2}-7t^{-3}+t^{-4}$
Conway polynomial	$z^{8}+z^{6}+3z^{4}+4z^{2}+1$
Determinant	225
Signature	4
HOMFLY-PT polynomial	$z^{8}a^{-4}-z^{6}a^{-2}+5z^{6}a^{-4}-3z^{6}a^{-6}-3z^{4}a^{-2}+12z^{4}a^{-4}-9z^{4}a^{-6}+3z^{4}a^{-8}-3z^{2}a^{-2}+13z^{2}a^{-4}-9z^{2}a^{-6}+4z^{2}a^{-8}-z^{2}a^{-10}-a^{-2}+5a^{-4}-3a^{-6}$
Kauffman polynomial	$z^{11}a^{-5}+z^{11}a^{-7}+4z^{10}a^{-4}+10z^{10}a^{-6}+6z^{10}a^{-8}+6z^{9}a^{-3}+20z^{9}a^{-5}+28z^{9}a^{-7}+14z^{9}a^{-9}+4z^{8}a^{-2}+7z^{8}a^{-4}+12z^{8}a^{-6}+26z^{8}a^{-8}+17z^{8}a^{-10}+z^{7}a^{-1}-14z^{7}a^{-3}-51z^{7}a^{-5}-53z^{7}a^{-7}-5z^{7}a^{-9}+12z^{7}a^{-11}-13z^{6}a^{-2}-47z^{6}a^{-4}-85z^{6}a^{-6}-79z^{6}a^{-8}-23z^{6}a^{-10}+5z^{6}a^{-12}-3z^{5}a^{-1}+6z^{5}a^{-3}+26z^{5}a^{-5}+8z^{5}a^{-7}-24z^{5}a^{-9}-14z^{5}a^{-11}+z^{5}a^{-13}+15z^{4}a^{-2}+59z^{4}a^{-4}+91z^{4}a^{-6}+62z^{4}a^{-8}+12z^{4}a^{-10}-3z^{4}a^{-12}+3z^{3}a^{-1}+6z^{3}a^{-3}+12z^{3}a^{-5}+21z^{3}a^{-7}+18z^{3}a^{-9}+6z^{3}a^{-11}-7z^{2}a^{-2}-28z^{2}a^{-4}-33z^{2}a^{-6}-17z^{2}a^{-8}-5z^{2}a^{-10}-za^{-1}-4za^{-3}-9za^{-5}-7za^{-7}-2za^{-9}-za^{-11}+a^{-2}+5a^{-4}+3a^{-6}$

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