K14a2139

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a2139

Polynomial invariants

Jones polynomial	Data:K14a2139/Jones Polynomial
Alexander polynomial	$-t^{4}+12t^{3}-56t^{2}+131t-171+131t^{-1}-56t^{-2}+12t^{-3}-t^{-4}$
Conway polynomial	Data:K14a2139/Conway Polynomial
Determinant	Data:K14a2139/Determinant
Signature	Data:K14a2139/Signature
HOMFLY-PT polynomial	$-z^{8}a^{-2}-2z^{6}a^{-2}+4z^{6}a^{-4}+2z^{6}-a^{2}z^{4}-6z^{4}a^{-2}+7z^{4}a^{-4}-6z^{4}a^{-6}+2z^{4}-6z^{2}a^{-2}+8z^{2}a^{-4}-8z^{2}a^{-6}+4z^{2}a^{-8}+z^{2}+a^{2}-2a^{-2}+4a^{-4}-4a^{-6}+3a^{-8}-a^{-10}$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +9 z^{12} $Failed^{-1} +16 z^{12} $Failed^{-1} +7 z^{12} $Failed^{-1} +18 z^{11} $Failed^{-1} +35 z^{11} $Failed^{-1} +28 z^{11} $Failed^{-1} +11 z^{11} $Failed^{-1} +28 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} +16 z^{10} $Failed^{-1} +11 z^{10} $Failed^{-1} +21 z^{10}+15 \text{QuantumGroups$\grave{ }$a} z^9-7 z^9 $Failed^{-1} -55 z^9 $Failed^{-1} -45 z^9 $Failed^{-1} -4 z^9 $Failed^{-1} +8 z^9 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^2 z^8-90 z^8 $Failed^{-1} -82 z^8 $Failed^{-1} -52 z^8 $Failed^{-1} -15 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} -35 z^8+\text{QuantumGroups$\grave{ }$a}^3 z^7-31 \text{QuantumGroups$\grave{ }$a} z^7-53 z^7 $Failed^{-1} -21 z^7 $Failed^{-1} -10 z^7 $Failed^{-1} -28 z^7 $Failed^{-1} -17 z^7 $Failed^{-1} +z^7 $Failed^{-1} -11 \text{QuantumGroups$\grave{ }$a}^2 z^6+54 z^6 $Failed^{-1} +67 z^6 $Failed^{-1} +36 z^6 $Failed^{-1} -5 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +6 z^6-\text{QuantumGroups$\grave{ }$a}^3 z^5+21 \text{QuantumGroups$\grave{ }$a} z^5+57 z^5 $Failed^{-1} +67 z^5 $Failed^{-1} +59 z^5 $Failed^{-1} +41 z^5 $Failed^{-1} +11 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^2 z^4+2 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} +20 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} +10 z^4-4 \text{QuantumGroups$\grave{ }$a} z^3-24 z^3 $Failed^{-1} -39 z^3 $Failed^{-1} -36 z^3 $Failed^{-1} -22 z^3 $Failed^{-1} -2 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^2 z^2-11 z^2 $Failed^{-1} -15 z^2 $Failed^{-1} -17 z^2 $Failed^{-1} -14 z^2 $Failed^{-1} -5 z^2 $Failed^{-1} -3 z^2+4 z $Failed^{-1} +8 z $Failed^{-1} +7 z $Failed^{-1} +4 z $Failed^{-1} -z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2+2 $Failed^{-1} +4 $Failed^{-1} +4 $Failed^{-1} +3 $Failed^{-1} + $Failed^{-1} }

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