K14a1389

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a1389

Polynomial invariants

Jones polynomial	Data:K14a1389/Jones Polynomial
Alexander polynomial	$2t^{4}-15t^{3}+54t^{2}-112t+143-112t^{-1}+54t^{-2}-15t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a1389/Conway Polynomial
Determinant	Data:K14a1389/Determinant
Signature	Data:K14a1389/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}-a^{4}z^{6}+4a^{2}z^{6}-3z^{6}a^{-2}+z^{6}-3a^{4}z^{4}+11a^{2}z^{4}-6z^{4}a^{-2}+3z^{4}a^{-4}-z^{4}-5a^{4}z^{2}+12a^{2}z^{2}-6z^{2}a^{-2}+5z^{2}a^{-4}-z^{2}a^{-6}-4z^{2}-2a^{4}+5a^{2}-2a^{-2}+3a^{-4}-a^{-6}-2$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+7 z^{12} $Failed^{-1} +16 z^{12}+17 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+32 \text{QuantumGroups$\grave{ }$a} z^{11}+26 z^{11} $Failed^{-1} +11 z^{11} $Failed^{-1} +17 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+11 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+11 z^{10} $Failed^{-1} +11 z^{10} $Failed^{-1} -6 z^{10}+10 \text{QuantumGroups$\grave{ }$a}^5 z^9-38 \text{QuantumGroups$\grave{ }$a}^3 z^9-95 \text{QuantumGroups$\grave{ }$a} z^9-63 z^9 $Failed^{-1} -8 z^9 $Failed^{-1} +8 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-51 \text{QuantumGroups$\grave{ }$a}^4 z^8-91 \text{QuantumGroups$\grave{ }$a}^2 z^8-45 z^8 $Failed^{-1} -16 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} -61 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-27 \text{QuantumGroups$\grave{ }$a}^5 z^7+26 \text{QuantumGroups$\grave{ }$a}^3 z^7+107 \text{QuantumGroups$\grave{ }$a} z^7+55 z^7 $Failed^{-1} -16 z^7 $Failed^{-1} -17 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+69 \text{QuantumGroups$\grave{ }$a}^4 z^6+158 \text{QuantumGroups$\grave{ }$a}^2 z^6+38 z^6 $Failed^{-1} -4 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +110 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+26 \text{QuantumGroups$\grave{ }$a}^5 z^5+8 \text{QuantumGroups$\grave{ }$a}^3 z^5-51 \text{QuantumGroups$\grave{ }$a} z^5-25 z^5 $Failed^{-1} +18 z^5 $Failed^{-1} +10 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^6 z^4-55 \text{QuantumGroups$\grave{ }$a}^4 z^4-122 \text{QuantumGroups$\grave{ }$a}^2 z^4-10 z^4 $Failed^{-1} +18 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} -79 z^4+2 \text{QuantumGroups$\grave{ }$a}^7 z^3-15 \text{QuantumGroups$\grave{ }$a}^5 z^3-17 \text{QuantumGroups$\grave{ }$a}^3 z^3+10 \text{QuantumGroups$\grave{ }$a} z^3+7 z^3 $Failed^{-1} -6 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} +20 \text{QuantumGroups$\grave{ }$a}^4 z^2+43 \text{QuantumGroups$\grave{ }$a}^2 z^2-5 z^2 $Failed^{-1} -12 z^2 $Failed^{-1} -5 z^2 $Failed^{-1} +25 z^2+3 \text{QuantumGroups$\grave{ }$a}^5 z+4 \text{QuantumGroups$\grave{ }$a}^3 z-\text{QuantumGroups$\grave{ }$a} z-2 z $Failed^{-1} -z $Failed^{-1} -z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4-5 \text{QuantumGroups$\grave{ }$a}^2+2 $Failed^{-1} +3 $Failed^{-1} + $Failed^{-1} -2}

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