K14a7537

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a7537

Polynomial invariants

Jones polynomial	Data:K14a7537/Jones Polynomial
Alexander polynomial	$-4t^{4}+17t^{3}-35t^{2}+48t-51+48t^{-1}-35t^{-2}+17t^{-3}-4t^{-4}$
Conway polynomial	Data:K14a7537/Conway Polynomial
Determinant	Data:K14a7537/Determinant
Signature	Data:K14a7537/Signature
HOMFLY-PT polynomial	$-a^{2}z^{8}-z^{8}a^{-2}-2z^{8}+a^{4}z^{6}-4a^{2}z^{6}-3z^{6}a^{-2}+z^{6}a^{-4}-10z^{6}+4a^{4}z^{4}-4a^{2}z^{4}+z^{4}a^{-2}+3z^{4}a^{-4}-17z^{4}+4a^{4}z^{2}-a^{2}z^{2}+7z^{2}a^{-2}+z^{2}a^{-4}-14z^{2}+a^{4}+a^{2}+5a^{-2}-a^{-4}-5$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 z^{13} $Failed^{-1} +2 z^{13} $Failed^{-1} +12 z^{12} $Failed^{-1} +5 z^{12} $Failed^{-1} +7 z^{12}+13 \text{QuantumGroups$\grave{ }$a} z^{11}+12 z^{11} $Failed^{-1} +3 z^{11} $Failed^{-1} +4 z^{11} $Failed^{-1} +16 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-52 z^{10} $Failed^{-1} -26 z^{10} $Failed^{-1} +z^{10} $Failed^{-1} -9 z^{10}+16 \text{QuantumGroups$\grave{ }$a}^3 z^9-38 \text{QuantumGroups$\grave{ }$a} z^9-89 z^9 $Failed^{-1} -60 z^9 $Failed^{-1} -25 z^9 $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^4 z^8-44 \text{QuantumGroups$\grave{ }$a}^2 z^8+46 z^8 $Failed^{-1} +38 z^8 $Failed^{-1} -6 z^8 $Failed^{-1} -56 z^8+10 \text{QuantumGroups$\grave{ }$a}^5 z^7-37 \text{QuantumGroups$\grave{ }$a}^3 z^7+18 \text{QuantumGroups$\grave{ }$a} z^7+147 z^7 $Failed^{-1} +137 z^7 $Failed^{-1} +55 z^7 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^6 z^6-28 \text{QuantumGroups$\grave{ }$a}^4 z^6+27 \text{QuantumGroups$\grave{ }$a}^2 z^6+46 z^6 $Failed^{-1} -4 z^6 $Failed^{-1} +13 z^6 $Failed^{-1} +124 z^6+3 \text{QuantumGroups$\grave{ }$a}^7 z^5-14 \text{QuantumGroups$\grave{ }$a}^5 z^5+19 \text{QuantumGroups$\grave{ }$a}^3 z^5+7 \text{QuantumGroups$\grave{ }$a} z^5-82 z^5 $Failed^{-1} -103 z^5 $Failed^{-1} -50 z^5 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^4-5 \text{QuantumGroups$\grave{ }$a}^6 z^4+20 \text{QuantumGroups$\grave{ }$a}^4 z^4-6 \text{QuantumGroups$\grave{ }$a}^2 z^4-74 z^4 $Failed^{-1} -21 z^4 $Failed^{-1} -12 z^4 $Failed^{-1} -97 z^4-2 \text{QuantumGroups$\grave{ }$a}^7 z^3+9 \text{QuantumGroups$\grave{ }$a}^5 z^3-\text{QuantumGroups$\grave{ }$a}^3 z^3-7 \text{QuantumGroups$\grave{ }$a} z^3+11 z^3 $Failed^{-1} +22 z^3 $Failed^{-1} +16 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8 z^2+2 \text{QuantumGroups$\grave{ }$a}^6 z^2-7 \text{QuantumGroups$\grave{ }$a}^4 z^2+\text{QuantumGroups$\grave{ }$a}^2 z^2+31 z^2 $Failed^{-1} +10 z^2 $Failed^{-1} +4 z^2 $Failed^{-1} +36 z^2-2 \text{QuantumGroups$\grave{ }$a}^5 z-\text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a} z+2 z $Failed^{-1} +z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4-\text{QuantumGroups$\grave{ }$a}^2-5 $Failed^{-1} - $Failed^{-1} -5}

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