K14a6691

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a6691

Polynomial invariants

Jones polynomial	Data:K14a6691/Jones Polynomial
Alexander polynomial	$2t^{4}-14t^{3}+48t^{2}-96t+121-96t^{-1}+48t^{-2}-14t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a6691/Conway Polynomial
Determinant	Data:K14a6691/Determinant
Signature	Data:K14a6691/Signature
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}-2a^{2}z^{6}+3z^{6}a^{-2}-2z^{6}a^{-4}+3z^{6}+a^{4}z^{4}-5a^{2}z^{4}+6z^{4}a^{-2}-5z^{4}a^{-4}+z^{4}a^{-6}+6z^{4}+a^{4}z^{2}-5a^{2}z^{2}+5z^{2}a^{-2}-5z^{2}a^{-4}+z^{2}a^{-6}+5z^{2}-a^{2}+a^{-2}-a^{-4}+2$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle z^{13} $Failed^{-1} +z^{13} $Failed^{-1} +10 z^{12} $Failed^{-1} +5 z^{12} $Failed^{-1} +5 z^{12}+11 \text{QuantumGroups$\grave{ }$a} z^{11}+25 z^{11} $Failed^{-1} +24 z^{11} $Failed^{-1} +10 z^{11} $Failed^{-1} +15 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+11 z^{10} $Failed^{-1} +13 z^{10} $Failed^{-1} +10 z^{10} $Failed^{-1} +23 z^{10}+15 \text{QuantumGroups$\grave{ }$a}^3 z^9+3 \text{QuantumGroups$\grave{ }$a} z^9-55 z^9 $Failed^{-1} -71 z^9 $Failed^{-1} -23 z^9 $Failed^{-1} +5 z^9 $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^4 z^8-13 \text{QuantumGroups$\grave{ }$a}^2 z^8-105 z^8 $Failed^{-1} -91 z^8 $Failed^{-1} -36 z^8 $Failed^{-1} +z^8 $Failed^{-1} -75 z^8+5 \text{QuantumGroups$\grave{ }$a}^5 z^7-21 \text{QuantumGroups$\grave{ }$a}^3 z^7-39 \text{QuantumGroups$\grave{ }$a} z^7+20 z^7 $Failed^{-1} +46 z^7 $Failed^{-1} -5 z^7 $Failed^{-1} -18 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^6-19 \text{QuantumGroups$\grave{ }$a}^4 z^6-15 \text{QuantumGroups$\grave{ }$a}^2 z^6+154 z^6 $Failed^{-1} +131 z^6 $Failed^{-1} +41 z^6 $Failed^{-1} -3 z^6 $Failed^{-1} +72 z^6-8 \text{QuantumGroups$\grave{ }$a}^5 z^5+3 \text{QuantumGroups$\grave{ }$a}^3 z^5+36 \text{QuantumGroups$\grave{ }$a} z^5+27 z^5 $Failed^{-1} +17 z^5 $Failed^{-1} +34 z^5 $Failed^{-1} +19 z^5 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6 z^4+10 \text{QuantumGroups$\grave{ }$a}^4 z^4+22 \text{QuantumGroups$\grave{ }$a}^2 z^4-91 z^4 $Failed^{-1} -77 z^4 $Failed^{-1} -19 z^4 $Failed^{-1} +2 z^4 $Failed^{-1} -24 z^4+3 \text{QuantumGroups$\grave{ }$a}^5 z^3+5 \text{QuantumGroups$\grave{ }$a}^3 z^3-9 \text{QuantumGroups$\grave{ }$a} z^3-21 z^3 $Failed^{-1} -24 z^3 $Failed^{-1} -20 z^3 $Failed^{-1} -6 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4 z^2-9 \text{QuantumGroups$\grave{ }$a}^2 z^2+21 z^2 $Failed^{-1} +18 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} -z^2-\text{QuantumGroups$\grave{ }$a}^3 z+4 z $Failed^{-1} +6 z $Failed^{-1} +3 z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} - $Failed^{-1} +2}

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