K13a4304

Knotscape

Decorative quasi-Celtic knot

Knotscape

Decorative quasi-Celtic knot

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4304

Polynomial invariants

Jones polynomial	Data:K13a4304/Jones Polynomial
Alexander polynomial	$16t^{2}-52t+73-52t^{-1}+16t^{-2}$
Conway polynomial	Data:K13a4304/Conway Polynomial
Determinant	209
Signature	4
HOMFLY-PT polynomial	$z^{4}a^{-4}+4z^{4}a^{-6}+6z^{4}a^{-8}+4z^{4}a^{-10}+z^{4}a^{-12}+4z^{2}a^{-6}+8z^{2}a^{-8}+3z^{2}a^{-10}-2z^{2}a^{-12}-z^{2}a^{-14}+3a^{-8}-2a^{-12}$
Kauffman polynomial	$z^{12}a^{-12}+z^{12}a^{-14}+4z^{11}a^{-11}+7z^{11}a^{-13}+3z^{11}a^{-15}+10z^{10}a^{-10}+13z^{10}a^{-12}+6z^{10}a^{-14}+3z^{10}a^{-16}+16z^{9}a^{-9}+13z^{9}a^{-11}-15z^{9}a^{-13}-11z^{9}a^{-15}+z^{9}a^{-17}+19z^{8}a^{-8}-5z^{8}a^{-10}-48z^{8}a^{-12}-41z^{8}a^{-14}-17z^{8}a^{-16}+16z^{7}a^{-7}-23z^{7}a^{-9}-71z^{7}a^{-11}-23z^{7}a^{-13}+3z^{7}a^{-15}-6z^{7}a^{-17}+10z^{6}a^{-6}-32z^{6}a^{-8}-37z^{6}a^{-10}+34z^{6}a^{-12}+62z^{6}a^{-14}+33z^{6}a^{-16}+4z^{5}a^{-5}-20z^{5}a^{-7}-2z^{5}a^{-9}+76z^{5}a^{-11}+66z^{5}a^{-13}+25z^{5}a^{-15}+13z^{5}a^{-17}+z^{4}a^{-4}-8z^{4}a^{-6}+21z^{4}a^{-8}+32z^{4}a^{-10}+2z^{4}a^{-12}-24z^{4}a^{-14}-24z^{4}a^{-16}+8z^{3}a^{-7}-34z^{3}a^{-11}-38z^{3}a^{-13}-24z^{3}a^{-15}-12z^{3}a^{-17}+4z^{2}a^{-6}-14z^{2}a^{-8}-9z^{2}a^{-10}+4z^{2}a^{-12}-z^{2}a^{-14}+4z^{2}a^{-16}+8za^{-11}+8za^{-13}+4za^{-15}+4za^{-17}+3a^{-8}-2a^{-12}$

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.