K14a474

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a474

Polynomial invariants

Jones polynomial	Data:K14a474/Jones Polynomial
Alexander polynomial	$t^{5}-7t^{4}+24t^{3}-53t^{2}+82t-93+82t^{-1}-53t^{-2}+24t^{-3}-7t^{-4}+t^{-5}$
Conway polynomial	Data:K14a474/Conway Polynomial
Determinant	Data:K14a474/Determinant
Signature	Data:K14a474/Signature
HOMFLY-PT polynomial	$a^{2}z^{10}-a^{4}z^{8}+7a^{2}z^{8}-3z^{8}-5a^{4}z^{6}+22a^{2}z^{6}+3z^{6}a^{-2}-17z^{6}-10a^{4}z^{4}+37a^{2}z^{4}+13z^{4}a^{-2}-z^{4}a^{-4}-38z^{4}-9a^{4}z^{2}+32a^{2}z^{2}+19z^{2}a^{-2}-3z^{2}a^{-4}-40z^{2}-3a^{4}+12a^{2}+10a^{-2}-2a^{-4}-16$
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 \text{QuantumGroups$\grave{ }$a} z^{13}+z^{13} $Failed^{-1} +7 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+4 z^{12} $Failed^{-1} +11 z^{12}+19 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+35 \text{QuantumGroups$\grave{ }$a} z^{11}+22 z^{11} $Failed^{-1} +6 z^{11} $Failed^{-1} +28 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+35 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+5 z^{10} $Failed^{-1} +4 z^{10} $Failed^{-1} +8 z^{10}+27 \text{QuantumGroups$\grave{ }$a}^5 z^9-15 \text{QuantumGroups$\grave{ }$a}^3 z^9-109 \text{QuantumGroups$\grave{ }$a} z^9-90 z^9 $Failed^{-1} -22 z^9 $Failed^{-1} +z^9 $Failed^{-1} +19 \text{QuantumGroups$\grave{ }$a}^6 z^8-57 \text{QuantumGroups$\grave{ }$a}^4 z^8-176 \text{QuantumGroups$\grave{ }$a}^2 z^8-80 z^8 $Failed^{-1} -20 z^8 $Failed^{-1} -160 z^8+10 \text{QuantumGroups$\grave{ }$a}^7 z^7-54 \text{QuantumGroups$\grave{ }$a}^5 z^7-65 \text{QuantumGroups$\grave{ }$a}^3 z^7+69 \text{QuantumGroups$\grave{ }$a} z^7+93 z^7 $Failed^{-1} +18 z^7 $Failed^{-1} -5 z^7 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^8 z^6-30 \text{QuantumGroups$\grave{ }$a}^6 z^6+40 \text{QuantumGroups$\grave{ }$a}^4 z^6+247 \text{QuantumGroups$\grave{ }$a}^2 z^6+166 z^6 $Failed^{-1} +37 z^6 $Failed^{-1} +302 z^6+\text{QuantumGroups$\grave{ }$a}^9 z^5-10 \text{QuantumGroups$\grave{ }$a}^7 z^5+49 \text{QuantumGroups$\grave{ }$a}^5 z^5+105 \text{QuantumGroups$\grave{ }$a}^3 z^5+35 \text{QuantumGroups$\grave{ }$a} z^5-6 z^5 $Failed^{-1} +13 z^5 $Failed^{-1} +9 z^5 $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^8 z^4+24 \text{QuantumGroups$\grave{ }$a}^6 z^4-16 \text{QuantumGroups$\grave{ }$a}^4 z^4-177 \text{QuantumGroups$\grave{ }$a}^2 z^4-143 z^4 $Failed^{-1} -32 z^4 $Failed^{-1} -245 z^4-\text{QuantumGroups$\grave{ }$a}^9 z^3+4 \text{QuantumGroups$\grave{ }$a}^7 z^3-22 \text{QuantumGroups$\grave{ }$a}^5 z^3-62 \text{QuantumGroups$\grave{ }$a}^3 z^3-48 \text{QuantumGroups$\grave{ }$a} z^3-27 z^3 $Failed^{-1} -21 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} -7 \text{QuantumGroups$\grave{ }$a}^6 z^2+8 \text{QuantumGroups$\grave{ }$a}^4 z^2+69 \text{QuantumGroups$\grave{ }$a}^2 z^2+59 z^2 $Failed^{-1} +13 z^2 $Failed^{-1} +100 z^2+5 \text{QuantumGroups$\grave{ }$a}^5 z+13 \text{QuantumGroups$\grave{ }$a}^3 z+12 \text{QuantumGroups$\grave{ }$a} z+8 z $Failed^{-1} +6 z $Failed^{-1} +2 z $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4-12 \text{QuantumGroups$\grave{ }$a}^2-10 $Failed^{-1} -2 $Failed^{-1} -16}

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