K14a7519

Knot presentations

Dowker-Thistlethwaite code

4 12 16 20 18 14 2 10 28 24 26 6 8 22

Notes on presentations of K14a7519

Polynomial invariants

Jones polynomial	Data:K14a7519/Jones Polynomial
Alexander polynomial	$-2t^{4}+16t^{3}-55t^{2}+105t-127+105t^{-1}-55t^{-2}+16t^{-3}-2t^{-4}$
Conway polynomial	Data:K14a7519/Conway Polynomial
Determinant	Data:K14a7519/Determinant
Signature	Data:K14a7519/Signature
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}a^{-4}-2z^{6}a^{-2}-2z^{6}a^{-4}+2z^{6}a^{-6}+2z^{6}-a^{2}z^{4}-3z^{4}a^{-2}-2z^{4}a^{-4}+4z^{4}a^{-6}-z^{4}a^{-8}+4z^{4}-a^{2}z^{2}-5z^{2}a^{-2}+2z^{2}a^{-6}-z^{2}a^{-8}+2z^{2}+a^{2}-3a^{-2}+2a^{-4}+1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +7 z^{12} $Failed^{-1} +16 z^{12} $Failed^{-1} +9 z^{12} $Failed^{-1} +11 z^{11} $Failed^{-1} +24 z^{11} $Failed^{-1} +30 z^{11} $Failed^{-1} +17 z^{11} $Failed^{-1} +7 z^{10} $Failed^{-1} -18 z^{10} $Failed^{-1} +5 z^{10} $Failed^{-1} +18 z^{10} $Failed^{-1} +12 z^{10}+10 \text{QuantumGroups$\grave{ }$a} z^9-7 z^9 $Failed^{-1} -70 z^9 $Failed^{-1} -106 z^9 $Failed^{-1} -41 z^9 $Failed^{-1} +12 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^2 z^8-35 z^8 $Failed^{-1} -35 z^8 $Failed^{-1} -79 z^8 $Failed^{-1} -53 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -16 z^8+\text{QuantumGroups$\grave{ }$a}^3 z^7-23 \text{QuantumGroups$\grave{ }$a} z^7-24 z^7 $Failed^{-1} +79 z^7 $Failed^{-1} +138 z^7 $Failed^{-1} +25 z^7 $Failed^{-1} -33 z^7 $Failed^{-1} +z^7 $Failed^{-1} -13 \text{QuantumGroups$\grave{ }$a}^2 z^6+18 z^6 $Failed^{-1} +86 z^6 $Failed^{-1} +130 z^6 $Failed^{-1} +52 z^6 $Failed^{-1} -12 z^6 $Failed^{-1} -15 z^6-2 \text{QuantumGroups$\grave{ }$a}^3 z^5+15 \text{QuantumGroups$\grave{ }$a} z^5+23 z^5 $Failed^{-1} -43 z^5 $Failed^{-1} -70 z^5 $Failed^{-1} +4 z^5 $Failed^{-1} +23 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^2 z^4+10 z^4 $Failed^{-1} -48 z^4 $Failed^{-1} -71 z^4 $Failed^{-1} -25 z^4 $Failed^{-1} +4 z^4 $Failed^{-1} +27 z^4+\text{QuantumGroups$\grave{ }$a}^3 z^3-3 \text{QuantumGroups$\grave{ }$a} z^3-11 z^3 $Failed^{-1} +7 z^3 $Failed^{-1} +18 z^3 $Failed^{-1} -2 z^3 $Failed^{-1} -6 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^2 z^2-15 z^2 $Failed^{-1} +2 z^2 $Failed^{-1} +13 z^2 $Failed^{-1} +5 z^2 $Failed^{-1} -11 z^2+\text{QuantumGroups$\grave{ }$a} z+4 z $Failed^{-1} +z $Failed^{-1} -3 z $Failed^{-1} -z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2+3 $Failed^{-1} +2 $Failed^{-1} +1}

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