K14a13086

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13086

Polynomial invariants

Jones polynomial	Data:K14a13086/Jones Polynomial
Alexander polynomial	$-2t^{4}+15t^{3}-50t^{2}+91t-107+91t^{-1}-50t^{-2}+15t^{-3}-2t^{-4}$
Conway polynomial	Data:K14a13086/Conway Polynomial
Determinant	Data:K14a13086/Determinant
Signature	Data:K14a13086/Signature
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}a^{-4}-z^{6}a^{-2}-4z^{6}a^{-4}+z^{6}a^{-6}+3z^{6}-3a^{2}z^{4}+4z^{4}a^{-2}-10z^{4}a^{-4}+3z^{4}a^{-6}+6z^{4}+a^{4}z^{2}-6a^{2}z^{2}+9z^{2}a^{-2}-13z^{2}a^{-4}+4z^{2}a^{-6}-z^{2}+2a^{4}-a^{2}+7a^{-2}-5a^{-4}+2a^{-6}-4$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +14 z^{12} $Failed^{-1} +9 z^{12} $Failed^{-1} +5 z^{12}+7 \text{QuantumGroups$\grave{ }$a} z^{11}+13 z^{11} $Failed^{-1} +25 z^{11} $Failed^{-1} +19 z^{11} $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-25 z^{10} $Failed^{-1} +4 z^{10} $Failed^{-1} +23 z^{10} $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^3 z^9-17 \text{QuantumGroups$\grave{ }$a} z^9-50 z^9 $Failed^{-1} -96 z^9 $Failed^{-1} -48 z^9 $Failed^{-1} +18 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^8-20 \text{QuantumGroups$\grave{ }$a}^2 z^8-17 z^8 $Failed^{-1} -83 z^8 $Failed^{-1} -70 z^8 $Failed^{-1} +10 z^8 $Failed^{-1} -35 z^8-11 \text{QuantumGroups$\grave{ }$a}^3 z^7+10 \text{QuantumGroups$\grave{ }$a} z^7+66 z^7 $Failed^{-1} +139 z^7 $Failed^{-1} +42 z^7 $Failed^{-1} -48 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -5 \text{QuantumGroups$\grave{ }$a}^4 z^6+21 \text{QuantumGroups$\grave{ }$a}^2 z^6+94 z^6 $Failed^{-1} +177 z^6 $Failed^{-1} +94 z^6 $Failed^{-1} -21 z^6 $Failed^{-1} +z^6 $Failed^{-1} +59 z^6+12 \text{QuantumGroups$\grave{ }$a}^3 z^5-13 \text{QuantumGroups$\grave{ }$a} z^5-67 z^5 $Failed^{-1} -88 z^5 $Failed^{-1} +11 z^5 $Failed^{-1} +50 z^5 $Failed^{-1} -7 z^5 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^4 z^4-9 \text{QuantumGroups$\grave{ }$a}^2 z^4-126 z^4 $Failed^{-1} -150 z^4 $Failed^{-1} -55 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -62 z^4-3 \text{QuantumGroups$\grave{ }$a}^3 z^3+23 \text{QuantumGroups$\grave{ }$a} z^3+44 z^3 $Failed^{-1} +20 z^3 $Failed^{-1} -18 z^3 $Failed^{-1} -20 z^3 $Failed^{-1} -7 \text{QuantumGroups$\grave{ }$a}^4 z^2+\text{QuantumGroups$\grave{ }$a}^2 z^2+62 z^2 $Failed^{-1} +54 z^2 $Failed^{-1} +18 z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +36 z^2-\text{QuantumGroups$\grave{ }$a}^3 z-11 \text{QuantumGroups$\grave{ }$a} z-15 z $Failed^{-1} -5 z $Failed^{-1} +2 z $Failed^{-1} +2 z $Failed^{-1} +2 \text{QuantumGroups$\grave{ }$a}^4+\text{QuantumGroups$\grave{ }$a}^2-7 $Failed^{-1} -5 $Failed^{-1} -2 $Failed^{-1} -4}

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