K14a1398

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a1398

Polynomial invariants

Jones polynomial	Data:K14a1398/Jones Polynomial
Alexander polynomial	$t^{5}-8t^{4}+31t^{3}-74t^{2}+123t-145+123t^{-1}-74t^{-2}+31t^{-3}-8t^{-4}+t^{-5}$
Conway polynomial	Data:K14a1398/Conway Polynomial
Determinant	Data:K14a1398/Determinant
Signature	Data:K14a1398/Signature
HOMFLY-PT polynomial	$a^{2}z^{10}-2a^{4}z^{8}+6a^{2}z^{8}-2z^{8}+a^{6}z^{6}-9a^{4}z^{6}+18a^{2}z^{6}+z^{6}a^{-2}-9z^{6}+3a^{6}z^{4}-17a^{4}z^{4}+30a^{2}z^{4}+3z^{4}a^{-2}-17z^{4}+3a^{6}z^{2}-14a^{4}z^{2}+26a^{2}z^{2}+3z^{2}a^{-2}-15z^{2}-4a^{4}+9a^{2}+a^{-2}-5$
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}^3 z^{13}+2 \text{QuantumGroups$\grave{ }$a} z^{13}+11 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+19 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+8 z^{12}+25 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+52 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+40 \text{QuantumGroups$\grave{ }$a} z^{11}+13 z^{11} $Failed^{-1} +31 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+49 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+29 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+11 z^{10} $Failed^{-1} +22 z^{10}+24 \text{QuantumGroups$\grave{ }$a}^7 z^9-11 \text{QuantumGroups$\grave{ }$a}^5 z^9-104 \text{QuantumGroups$\grave{ }$a}^3 z^9-94 \text{QuantumGroups$\grave{ }$a} z^9-20 z^9 $Failed^{-1} +5 z^9 $Failed^{-1} +13 \text{QuantumGroups$\grave{ }$a}^8 z^8-52 \text{QuantumGroups$\grave{ }$a}^6 z^8-181 \text{QuantumGroups$\grave{ }$a}^4 z^8-204 \text{QuantumGroups$\grave{ }$a}^2 z^8-32 z^8 $Failed^{-1} +z^8 $Failed^{-1} -121 z^8+5 \text{QuantumGroups$\grave{ }$a}^9 z^7-39 \text{QuantumGroups$\grave{ }$a}^7 z^7-64 \text{QuantumGroups$\grave{ }$a}^5 z^7+\text{QuantumGroups$\grave{ }$a}^3 z^7+15 \text{QuantumGroups$\grave{ }$a} z^7-22 z^7 $Failed^{-1} -16 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^{10} z^6-17 \text{QuantumGroups$\grave{ }$a}^8 z^6+40 \text{QuantumGroups$\grave{ }$a}^6 z^6+206 \text{QuantumGroups$\grave{ }$a}^4 z^6+268 \text{QuantumGroups$\grave{ }$a}^2 z^6+33 z^6 $Failed^{-1} -3 z^6 $Failed^{-1} +156 z^6-6 \text{QuantumGroups$\grave{ }$a}^9 z^5+30 \text{QuantumGroups$\grave{ }$a}^7 z^5+95 \text{QuantumGroups$\grave{ }$a}^5 z^5+103 \text{QuantumGroups$\grave{ }$a}^3 z^5+83 \text{QuantumGroups$\grave{ }$a} z^5+58 z^5 $Failed^{-1} +19 z^5 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^{10} z^4+8 \text{QuantumGroups$\grave{ }$a}^8 z^4-17 \text{QuantumGroups$\grave{ }$a}^6 z^4-116 \text{QuantumGroups$\grave{ }$a}^4 z^4-163 \text{QuantumGroups$\grave{ }$a}^2 z^4-15 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} -91 z^4+2 \text{QuantumGroups$\grave{ }$a}^9 z^3-10 \text{QuantumGroups$\grave{ }$a}^7 z^3-49 \text{QuantumGroups$\grave{ }$a}^5 z^3-77 \text{QuantumGroups$\grave{ }$a}^3 z^3-68 \text{QuantumGroups$\grave{ }$a} z^3-38 z^3 $Failed^{-1} -10 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^8 z^2+5 \text{QuantumGroups$\grave{ }$a}^6 z^2+35 \text{QuantumGroups$\grave{ }$a}^4 z^2+53 \text{QuantumGroups$\grave{ }$a}^2 z^2+4 z^2 $Failed^{-1} -z^2 $Failed^{-1} +29 z^2+8 \text{QuantumGroups$\grave{ }$a}^5 z+18 \text{QuantumGroups$\grave{ }$a}^3 z+17 \text{QuantumGroups$\grave{ }$a} z+9 z $Failed^{-1} +2 z $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^4-9 \text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} -5}

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