K14a6858

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a6858

Polynomial invariants

Jones polynomial	Data:K14a6858/Jones Polynomial
Alexander polynomial	$-2t^{4}+15t^{3}-52t^{2}+105t-131+105t^{-1}-52t^{-2}+15t^{-3}-2t^{-4}$
Conway polynomial	Data:K14a6858/Conway Polynomial
Determinant	Data:K14a6858/Determinant
Signature	Data:K14a6858/Signature
HOMFLY-PT polynomial	$-z^{4}a^{8}-2z^{2}a^{8}-2a^{8}+2z^{6}a^{6}+6z^{4}a^{6}+10z^{2}a^{6}+6a^{6}-z^{8}a^{4}-3z^{6}a^{4}-8z^{4}a^{4}-11z^{2}a^{4}-6a^{4}-z^{8}a^{2}-2z^{6}a^{2}-2z^{4}a^{2}+z^{2}a^{2}+2a^{2}+2z^{6}+4z^{4}+3z^{2}+1-z^{4}a^{-2}-z^{2}a^{-2}$
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a}^5 z^{13}+2 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+8 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+16 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+8 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+14 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+27 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+27 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+14 \text{QuantumGroups$\grave{ }$a} z^{11}+14 \text{QuantumGroups$\grave{ }$a}^8 z^{10}+3 \text{QuantumGroups$\grave{ }$a}^6 z^{10}-19 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+7 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+15 z^{10}+9 \text{QuantumGroups$\grave{ }$a}^9 z^9-35 \text{QuantumGroups$\grave{ }$a}^7 z^9-99 \text{QuantumGroups$\grave{ }$a}^5 z^9-87 \text{QuantumGroups$\grave{ }$a}^3 z^9-21 \text{QuantumGroups$\grave{ }$a} z^9+11 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^{10} z^8-42 \text{QuantumGroups$\grave{ }$a}^8 z^8-62 \text{QuantumGroups$\grave{ }$a}^6 z^8-35 \text{QuantumGroups$\grave{ }$a}^4 z^8-55 \text{QuantumGroups$\grave{ }$a}^2 z^8+5 z^8 $Failed^{-1} -31 z^8+\text{QuantumGroups$\grave{ }$a}^{11} z^7-25 \text{QuantumGroups$\grave{ }$a}^9 z^7+38 \text{QuantumGroups$\grave{ }$a}^7 z^7+157 \text{QuantumGroups$\grave{ }$a}^5 z^7+116 \text{QuantumGroups$\grave{ }$a}^3 z^7-4 \text{QuantumGroups$\grave{ }$a} z^7-26 z^7 $Failed^{-1} +z^7 $Failed^{-1} -11 \text{QuantumGroups$\grave{ }$a}^{10} z^6+55 \text{QuantumGroups$\grave{ }$a}^8 z^6+131 \text{QuantumGroups$\grave{ }$a}^6 z^6+111 \text{QuantumGroups$\grave{ }$a}^4 z^6+69 \text{QuantumGroups$\grave{ }$a}^2 z^6-12 z^6 $Failed^{-1} +11 z^6-3 \text{QuantumGroups$\grave{ }$a}^{11} z^5+22 \text{QuantumGroups$\grave{ }$a}^9 z^5-21 \text{QuantumGroups$\grave{ }$a}^7 z^5-124 \text{QuantumGroups$\grave{ }$a}^5 z^5-85 \text{QuantumGroups$\grave{ }$a}^3 z^5+11 \text{QuantumGroups$\grave{ }$a} z^5+16 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^{10} z^4-44 \text{QuantumGroups$\grave{ }$a}^8 z^4-121 \text{QuantumGroups$\grave{ }$a}^6 z^4-107 \text{QuantumGroups$\grave{ }$a}^4 z^4-39 \text{QuantumGroups$\grave{ }$a}^2 z^4+8 z^4 $Failed^{-1} +6 z^4+2 \text{QuantumGroups$\grave{ }$a}^{11} z^3-9 \text{QuantumGroups$\grave{ }$a}^9 z^3+2 \text{QuantumGroups$\grave{ }$a}^7 z^3+48 \text{QuantumGroups$\grave{ }$a}^5 z^3+39 \text{QuantumGroups$\grave{ }$a}^3 z^3-3 z^3 $Failed^{-1} +z^3 $Failed^{-1} +17 \text{QuantumGroups$\grave{ }$a}^8 z^2+47 \text{QuantumGroups$\grave{ }$a}^6 z^2+45 \text{QuantumGroups$\grave{ }$a}^4 z^2+13 \text{QuantumGroups$\grave{ }$a}^2 z^2-2 z^2 $Failed^{-1} -4 z^2+2 \text{QuantumGroups$\grave{ }$a}^9 z-8 \text{QuantumGroups$\grave{ }$a}^5 z-8 \text{QuantumGroups$\grave{ }$a}^3 z-2 \text{QuantumGroups$\grave{ }$a} z-2 \text{QuantumGroups$\grave{ }$a}^8-6 \text{QuantumGroups$\grave{ }$a}^6-6 \text{QuantumGroups$\grave{ }$a}^4-2 \text{QuantumGroups$\grave{ }$a}^2+1}

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