K14a18541

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18541

Polynomial invariants

Jones polynomial	Data:K14a18541/Jones Polynomial
Alexander polynomial	$3t^{4}-22t^{3}+69t^{2}-127t+155-127t^{-1}+69t^{-2}-22t^{-3}+3t^{-4}$
Conway polynomial	Data:K14a18541/Conway Polynomial
Determinant	Data:K14a18541/Determinant
Signature	Data:K14a18541/Signature
HOMFLY-PT polynomial	$2z^{8}a^{-2}+z^{8}-2a^{2}z^{6}+7z^{6}a^{-2}-3z^{6}a^{-4}+a^{4}z^{4}-3a^{2}z^{4}+11z^{4}a^{-2}-8z^{4}a^{-4}+z^{4}a^{-6}-5z^{4}+a^{4}z^{2}+9z^{2}a^{-2}-7z^{2}a^{-4}+2z^{2}a^{-6}-6z^{2}+a^{2}+4a^{-2}-3a^{-4}+a^{-6}-2$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 5 z^{13} $Failed^{-1} +5 z^{13} $Failed^{-1} +32 z^{12} $Failed^{-1} +15 z^{12} $Failed^{-1} +17 z^{12}+28 \text{QuantumGroups$\grave{ }$a} z^{11}+40 z^{11} $Failed^{-1} +30 z^{11} $Failed^{-1} +18 z^{11} $Failed^{-1} +30 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-71 z^{10} $Failed^{-1} -28 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} -z^{10}+23 \text{QuantumGroups$\grave{ }$a}^3 z^9-47 \text{QuantumGroups$\grave{ }$a} z^9-151 z^9 $Failed^{-1} -141 z^9 $Failed^{-1} -55 z^9 $Failed^{-1} +5 z^9 $Failed^{-1} +13 \text{QuantumGroups$\grave{ }$a}^4 z^8-58 \text{QuantumGroups$\grave{ }$a}^2 z^8+13 z^8 $Failed^{-1} -11 z^8 $Failed^{-1} -36 z^8 $Failed^{-1} +z^8 $Failed^{-1} -84 z^8+5 \text{QuantumGroups$\grave{ }$a}^5 z^7-40 \text{QuantumGroups$\grave{ }$a}^3 z^7+13 \text{QuantumGroups$\grave{ }$a} z^7+190 z^7 $Failed^{-1} +206 z^7 $Failed^{-1} +59 z^7 $Failed^{-1} -15 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^6-19 \text{QuantumGroups$\grave{ }$a}^4 z^6+43 \text{QuantumGroups$\grave{ }$a}^2 z^6+83 z^6 $Failed^{-1} +48 z^6 $Failed^{-1} +32 z^6 $Failed^{-1} -3 z^6 $Failed^{-1} +133 z^6-6 \text{QuantumGroups$\grave{ }$a}^5 z^5+26 \text{QuantumGroups$\grave{ }$a}^3 z^5+22 \text{QuantumGroups$\grave{ }$a} z^5-110 z^5 $Failed^{-1} -156 z^5 $Failed^{-1} -43 z^5 $Failed^{-1} +13 z^5 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6 z^4+8 \text{QuantumGroups$\grave{ }$a}^4 z^4-14 \text{QuantumGroups$\grave{ }$a}^2 z^4-89 z^4 $Failed^{-1} -48 z^4 $Failed^{-1} -13 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} -80 z^4+\text{QuantumGroups$\grave{ }$a}^5 z^3-9 \text{QuantumGroups$\grave{ }$a}^3 z^3-9 \text{QuantumGroups$\grave{ }$a} z^3+33 z^3 $Failed^{-1} +59 z^3 $Failed^{-1} +24 z^3 $Failed^{-1} -3 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4 z^2+5 \text{QuantumGroups$\grave{ }$a}^2 z^2+30 z^2 $Failed^{-1} +21 z^2 $Failed^{-1} +6 z^2 $Failed^{-1} -z^2 $Failed^{-1} +23 z^2+\text{QuantumGroups$\grave{ }$a}^3 z-6 z $Failed^{-1} -9 z $Failed^{-1} -4 z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2-4 $Failed^{-1} -3 $Failed^{-1} - $Failed^{-1} -2}

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