K13a1345

Knotscape

Symmetrical depiction as quasi-Celtic decorative knot

Rectangular quasi-Celtic decorative knot

Dowker-Thistlethwaite code

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

Jones polynomial	Data:K13a1345/Jones Polynomial
Alexander polynomial	[math]\displaystyle{ t^4-11 t^3+48 t^2-109 t+143-109 t^{-1} +48 t^{-2} -11 t^{-3} + t^{-4} }[/math]
Conway polynomial	Data:K13a1345/Conway Polynomial
Determinant	481
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ z^8-3 a^2 z^6-2 z^6 a^{-2} +2 z^6+3 a^4 z^4-4 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} +4 z^4-a^6 z^2+2 a^4 z^2-2 a^2 z^2-z^2 a^{-2} +2 z^2+1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 4 a^2 z^{12}+4 z^{12}+12 a^3 z^{11}+29 a z^{11}+17 z^{11} a^{-1} +16 a^4 z^{10}+39 a^2 z^{10}+30 z^{10} a^{-2} +53 z^{10}+12 a^5 z^9+8 a^3 z^9-14 a z^9+19 z^9 a^{-1} +29 z^9 a^{-3} +5 a^6 z^8-25 a^4 z^8-93 a^2 z^8-38 z^8 a^{-2} +17 z^8 a^{-4} -118 z^8+a^7 z^7-27 a^5 z^7-66 a^3 z^7-77 a z^7-91 z^7 a^{-1} -46 z^7 a^{-3} +6 z^7 a^{-5} -11 a^6 z^6+2 a^4 z^6+51 a^2 z^6+3 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} +63 z^6-2 a^7 z^5+24 a^5 z^5+68 a^3 z^5+81 a z^5+67 z^5 a^{-1} +24 z^5 a^{-3} -4 z^5 a^{-5} +9 a^6 z^4+14 a^4 z^4+8 z^4 a^{-2} +7 z^4 a^{-4} -4 z^4+a^7 z^3-9 a^5 z^3-25 a^3 z^3-27 a z^3-15 z^3 a^{-1} -3 z^3 a^{-3} -3 a^6 z^2-5 a^4 z^2-3 a^2 z^2-2 z^2 a^{-2} -3 z^2+a^5 z+3 a^3 z+3 a z+z a^{-1} +1 }[/math]

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