K14a1857

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a1857

Polynomial invariants

Jones polynomial	Data:K14a1857/Jones Polynomial
Alexander polynomial	$-3t^{4}+21t^{3}-66t^{2}+127t-157+127t^{-1}-66t^{-2}+21t^{-3}-3t^{-4}$
Conway polynomial	Data:K14a1857/Conway Polynomial
Determinant	Data:K14a1857/Determinant
Signature	Data:K14a1857/Signature
HOMFLY-PT polynomial	$-z^{4}a^{8}-2z^{2}a^{8}-2a^{8}+3z^{6}a^{6}+8z^{4}a^{6}+9z^{2}a^{6}+3a^{6}-2z^{8}a^{4}-7z^{6}a^{4}-11z^{4}a^{4}-6z^{2}a^{4}-z^{8}a^{2}-z^{6}a^{2}-z^{2}a^{2}-2a^{2}+2z^{6}+5z^{4}+6z^{2}+3-z^{4}a^{-2}-2z^{2}a^{-2}-a^{-2}$
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}+10 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+18 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+8 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+20 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+43 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+36 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+13 \text{QuantumGroups$\grave{ }$a} z^{11}+22 \text{QuantumGroups$\grave{ }$a}^8 z^{10}+31 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+15 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+18 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+12 z^{10}+14 \text{QuantumGroups$\grave{ }$a}^9 z^9-16 \text{QuantumGroups$\grave{ }$a}^7 z^9-89 \text{QuantumGroups$\grave{ }$a}^5 z^9-80 \text{QuantumGroups$\grave{ }$a}^3 z^9-13 \text{QuantumGroups$\grave{ }$a} z^9+8 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^{10} z^8-45 \text{QuantumGroups$\grave{ }$a}^8 z^8-120 \text{QuantumGroups$\grave{ }$a}^6 z^8-120 \text{QuantumGroups$\grave{ }$a}^4 z^8-73 \text{QuantumGroups$\grave{ }$a}^2 z^8+4 z^8 $Failed^{-1} -19 z^8+\text{QuantumGroups$\grave{ }$a}^{11} z^7-31 \text{QuantumGroups$\grave{ }$a}^9 z^7-43 \text{QuantumGroups$\grave{ }$a}^7 z^7+33 \text{QuantumGroups$\grave{ }$a}^5 z^7+53 \text{QuantumGroups$\grave{ }$a}^3 z^7-8 \text{QuantumGroups$\grave{ }$a} z^7-16 z^7 $Failed^{-1} +z^7 $Failed^{-1} -9 \text{QuantumGroups$\grave{ }$a}^{10} z^6+34 \text{QuantumGroups$\grave{ }$a}^8 z^6+119 \text{QuantumGroups$\grave{ }$a}^6 z^6+145 \text{QuantumGroups$\grave{ }$a}^4 z^6+83 \text{QuantumGroups$\grave{ }$a}^2 z^6-11 z^6 $Failed^{-1} +3 z^6-2 \text{QuantumGroups$\grave{ }$a}^{11} z^5+30 \text{QuantumGroups$\grave{ }$a}^9 z^5+65 \text{QuantumGroups$\grave{ }$a}^7 z^5+26 \text{QuantumGroups$\grave{ }$a}^5 z^5+\text{QuantumGroups$\grave{ }$a}^3 z^5+19 \text{QuantumGroups$\grave{ }$a} z^5+8 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^{10} z^4-18 \text{QuantumGroups$\grave{ }$a}^8 z^4-56 \text{QuantumGroups$\grave{ }$a}^6 z^4-67 \text{QuantumGroups$\grave{ }$a}^4 z^4-32 \text{QuantumGroups$\grave{ }$a}^2 z^4+11 z^4 $Failed^{-1} +13 z^4+\text{QuantumGroups$\grave{ }$a}^{11} z^3-19 \text{QuantumGroups$\grave{ }$a}^9 z^3-39 \text{QuantumGroups$\grave{ }$a}^7 z^3-21 \text{QuantumGroups$\grave{ }$a}^5 z^3-11 \text{QuantumGroups$\grave{ }$a}^3 z^3-11 \text{QuantumGroups$\grave{ }$a} z^3+z^3 $Failed^{-1} +3 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^{10} z^2+7 \text{QuantumGroups$\grave{ }$a}^8 z^2+15 \text{QuantumGroups$\grave{ }$a}^6 z^2+11 \text{QuantumGroups$\grave{ }$a}^4 z^2-3 \text{QuantumGroups$\grave{ }$a}^2 z^2-5 z^2 $Failed^{-1} -12 z^2+6 \text{QuantumGroups$\grave{ }$a}^9 z+9 \text{QuantumGroups$\grave{ }$a}^7 z+5 \text{QuantumGroups$\grave{ }$a}^5 z+4 \text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a} z-z $Failed^{-1} -z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^8-3 \text{QuantumGroups$\grave{ }$a}^6+2 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +3}

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