K14a2781

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a2781

Polynomial invariants

Jones polynomial	Data:K14a2781/Jones Polynomial
Alexander polynomial	$t^{5}-9t^{4}+35t^{3}-82t^{2}+133t-155+133t^{-1}-82t^{-2}+35t^{-3}-9t^{-4}+t^{-5}$
Conway polynomial	Data:K14a2781/Conway Polynomial
Determinant	Data:K14a2781/Determinant
Signature	Data:K14a2781/Signature
HOMFLY-PT polynomial	$a^{2}z^{10}-3a^{4}z^{8}+5a^{2}z^{8}-z^{8}+3a^{6}z^{6}-12a^{4}z^{6}+10a^{2}z^{6}-3z^{6}-a^{8}z^{4}+9a^{6}z^{4}-16a^{4}z^{4}+8a^{2}z^{4}-2z^{4}-2a^{8}z^{2}+8a^{6}z^{2}-7a^{4}z^{2}+a^{2}z^{2}+z^{2}-a^{8}+2a^{6}-a^{4}+1$
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 3 \text{QuantumGroups$\grave{ }$a}^5 z^{13}+3 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+12 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+25 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+13 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+21 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+49 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+52 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+24 \text{QuantumGroups$\grave{ }$a} z^{11}+21 \text{QuantumGroups$\grave{ }$a}^8 z^{10}+27 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+12 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+31 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+25 z^{10}+13 \text{QuantumGroups$\grave{ }$a}^9 z^9-24 \text{QuantumGroups$\grave{ }$a}^7 z^9-111 \text{QuantumGroups$\grave{ }$a}^5 z^9-114 \text{QuantumGroups$\grave{ }$a}^3 z^9-24 \text{QuantumGroups$\grave{ }$a} z^9+16 z^9 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^{10} z^8-44 \text{QuantumGroups$\grave{ }$a}^8 z^8-124 \text{QuantumGroups$\grave{ }$a}^6 z^8-154 \text{QuantumGroups$\grave{ }$a}^4 z^8-133 \text{QuantumGroups$\grave{ }$a}^2 z^8+6 z^8 $Failed^{-1} -48 z^8+\text{QuantumGroups$\grave{ }$a}^{11} z^7-28 \text{QuantumGroups$\grave{ }$a}^9 z^7-19 \text{QuantumGroups$\grave{ }$a}^7 z^7+57 \text{QuantumGroups$\grave{ }$a}^5 z^7+46 \text{QuantumGroups$\grave{ }$a}^3 z^7-34 \text{QuantumGroups$\grave{ }$a} z^7-32 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^{10} z^6+38 \text{QuantumGroups$\grave{ }$a}^8 z^6+153 \text{QuantumGroups$\grave{ }$a}^6 z^6+203 \text{QuantumGroups$\grave{ }$a}^4 z^6+134 \text{QuantumGroups$\grave{ }$a}^2 z^6-10 z^6 $Failed^{-1} +26 z^6-2 \text{QuantumGroups$\grave{ }$a}^{11} z^5+23 \text{QuantumGroups$\grave{ }$a}^9 z^5+45 \text{QuantumGroups$\grave{ }$a}^7 z^5+30 \text{QuantumGroups$\grave{ }$a}^5 z^5+40 \text{QuantumGroups$\grave{ }$a}^3 z^5+51 \text{QuantumGroups$\grave{ }$a} z^5+20 z^5 $Failed^{-1} -z^5 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^{10} z^4-22 \text{QuantumGroups$\grave{ }$a}^8 z^4-90 \text{QuantumGroups$\grave{ }$a}^6 z^4-107 \text{QuantumGroups$\grave{ }$a}^4 z^4-52 \text{QuantumGroups$\grave{ }$a}^2 z^4+4 z^4 $Failed^{-1} -3 z^4+\text{QuantumGroups$\grave{ }$a}^{11} z^3-11 \text{QuantumGroups$\grave{ }$a}^9 z^3-30 \text{QuantumGroups$\grave{ }$a}^7 z^3-34 \text{QuantumGroups$\grave{ }$a}^5 z^3-32 \text{QuantumGroups$\grave{ }$a}^3 z^3-20 \text{QuantumGroups$\grave{ }$a} z^3-4 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^{10} z^2+8 \text{QuantumGroups$\grave{ }$a}^8 z^2+25 \text{QuantumGroups$\grave{ }$a}^6 z^2+23 \text{QuantumGroups$\grave{ }$a}^4 z^2+5 \text{QuantumGroups$\grave{ }$a}^2 z^2-2 z^2+3 \text{QuantumGroups$\grave{ }$a}^9 z+7 \text{QuantumGroups$\grave{ }$a}^7 z+8 \text{QuantumGroups$\grave{ }$a}^5 z+6 \text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a} z-\text{QuantumGroups$\grave{ }$a}^8-2 \text{QuantumGroups$\grave{ }$a}^6-\text{QuantumGroups$\grave{ }$a}^4+1}

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