K14a3128

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a3128

Polynomial invariants

Jones polynomial	Data:K14a3128/Jones Polynomial
Alexander polynomial	$-t^{5}+8t^{4}-31t^{3}+75t^{2}-124t+147-124t^{-1}+75t^{-2}-31t^{-3}+8t^{-4}-t^{-5}$
Conway polynomial	Data:K14a3128/Conway Polynomial
Determinant	Data:K14a3128/Determinant
Signature	Data:K14a3128/Signature
HOMFLY-PT polynomial	$-z^{10}+2a^{2}z^{8}+2z^{8}a^{-2}-6z^{8}-a^{4}z^{6}+9a^{2}z^{6}+9z^{6}a^{-2}-z^{6}a^{-4}-18z^{6}-3a^{4}z^{4}+18a^{2}z^{4}+17z^{4}a^{-2}-3z^{4}a^{-4}-30z^{4}-4a^{4}z^{2}+18a^{2}z^{2}+15z^{2}a^{-2}-3z^{2}a^{-4}-26z^{2}-2a^{4}+7a^{2}+5a^{-2}-a^{-4}-8$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 3 \text{QuantumGroups$\grave{ }$a} z^{13}+3 z^{13} $Failed^{-1} +13 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+12 z^{12} $Failed^{-1} +25 z^{12}+23 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+49 \text{QuantumGroups$\grave{ }$a} z^{11}+46 z^{11} $Failed^{-1} +20 z^{11} $Failed^{-1} +22 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+17 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+16 z^{10} $Failed^{-1} +19 z^{10} $Failed^{-1} -8 z^{10}+13 \text{QuantumGroups$\grave{ }$a}^5 z^9-42 \text{QuantumGroups$\grave{ }$a}^3 z^9-146 \text{QuantumGroups$\grave{ }$a} z^9-134 z^9 $Failed^{-1} -31 z^9 $Failed^{-1} +12 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^6 z^8-52 \text{QuantumGroups$\grave{ }$a}^4 z^8-121 \text{QuantumGroups$\grave{ }$a}^2 z^8-105 z^8 $Failed^{-1} -40 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -124 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-28 \text{QuantumGroups$\grave{ }$a}^5 z^7+19 \text{QuantumGroups$\grave{ }$a}^3 z^7+156 \text{QuantumGroups$\grave{ }$a} z^7+138 z^7 $Failed^{-1} +3 z^7 $Failed^{-1} -26 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+52 \text{QuantumGroups$\grave{ }$a}^4 z^6+184 \text{QuantumGroups$\grave{ }$a}^2 z^6+150 z^6 $Failed^{-1} +30 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +231 z^6-2 \text{QuantumGroups$\grave{ }$a}^7 z^5+20 \text{QuantumGroups$\grave{ }$a}^5 z^5+5 \text{QuantumGroups$\grave{ }$a}^3 z^5-68 \text{QuantumGroups$\grave{ }$a} z^5-54 z^5 $Failed^{-1} +17 z^5 $Failed^{-1} +18 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^6 z^4-37 \text{QuantumGroups$\grave{ }$a}^4 z^4-135 \text{QuantumGroups$\grave{ }$a}^2 z^4-101 z^4 $Failed^{-1} -15 z^4 $Failed^{-1} +7 z^4 $Failed^{-1} -172 z^4+\text{QuantumGroups$\grave{ }$a}^7 z^3-8 \text{QuantumGroups$\grave{ }$a}^5 z^3-12 \text{QuantumGroups$\grave{ }$a}^3 z^3+6 \text{QuantumGroups$\grave{ }$a} z^3+2 z^3 $Failed^{-1} -14 z^3 $Failed^{-1} -6 z^3 $Failed^{-1} +z^3 $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^4 z^2+48 \text{QuantumGroups$\grave{ }$a}^2 z^2+34 z^2 $Failed^{-1} +5 z^2 $Failed^{-1} -z^2 $Failed^{-1} +62 z^2+2 \text{QuantumGroups$\grave{ }$a}^5 z+4 \text{QuantumGroups$\grave{ }$a}^3 z+3 \text{QuantumGroups$\grave{ }$a} z+3 z $Failed^{-1} +3 z $Failed^{-1} +z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^4-7 \text{QuantumGroups$\grave{ }$a}^2-5 $Failed^{-1} - $Failed^{-1} -8}

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