K14a13681

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13681

Polynomial invariants

Jones polynomial	Data:K14a13681/Jones Polynomial
Alexander polynomial	$-5t^{4}+31t^{3}-89t^{2}+160t-193+160t^{-1}-89t^{-2}+31t^{-3}-5t^{-4}$
Conway polynomial	Data:K14a13681/Conway Polynomial
Determinant	Data:K14a13681/Determinant
Signature	Data:K14a13681/Signature
HOMFLY-PT polynomial	$z^{6}a^{8}+z^{4}a^{8}-z^{8}a^{6}+4z^{4}a^{6}+2z^{2}a^{6}-2a^{6}-3z^{8}a^{4}-10z^{6}a^{4}-11z^{4}a^{4}-z^{2}a^{4}+3a^{4}-z^{8}a^{2}-z^{6}a^{2}+z^{4}a^{2}+z^{2}a^{2}+z^{6}+2z^{4}+z^{2}$
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 7 \text{QuantumGroups$\grave{ }$a}^7 z^{13}+7 \text{QuantumGroups$\grave{ }$a}^5 z^{13}+21 \text{QuantumGroups$\grave{ }$a}^8 z^{12}+46 \text{QuantumGroups$\grave{ }$a}^6 z^{12}+25 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+26 \text{QuantumGroups$\grave{ }$a}^9 z^{11}+50 \text{QuantumGroups$\grave{ }$a}^7 z^{11}+65 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+41 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+17 \text{QuantumGroups$\grave{ }$a}^{10} z^{10}-19 \text{QuantumGroups$\grave{ }$a}^8 z^{10}-70 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+7 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+41 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+6 \text{QuantumGroups$\grave{ }$a}^{11} z^9-64 \text{QuantumGroups$\grave{ }$a}^9 z^9-172 \text{QuantumGroups$\grave{ }$a}^7 z^9-197 \text{QuantumGroups$\grave{ }$a}^5 z^9-67 \text{QuantumGroups$\grave{ }$a}^3 z^9+28 \text{QuantumGroups$\grave{ }$a} z^9+\text{QuantumGroups$\grave{ }$a}^{12} z^8-45 \text{QuantumGroups$\grave{ }$a}^{10} z^8-57 \text{QuantumGroups$\grave{ }$a}^8 z^8-41 \text{QuantumGroups$\grave{ }$a}^6 z^8-123 \text{QuantumGroups$\grave{ }$a}^4 z^8-79 \text{QuantumGroups$\grave{ }$a}^2 z^8+14 z^8-14 \text{QuantumGroups$\grave{ }$a}^{11} z^7+46 \text{QuantumGroups$\grave{ }$a}^9 z^7+155 \text{QuantumGroups$\grave{ }$a}^7 z^7+176 \text{QuantumGroups$\grave{ }$a}^5 z^7+31 \text{QuantumGroups$\grave{ }$a}^3 z^7-45 \text{QuantumGroups$\grave{ }$a} z^7+5 z^7 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^{12} z^6+41 \text{QuantumGroups$\grave{ }$a}^{10} z^6+69 \text{QuantumGroups$\grave{ }$a}^8 z^6+86 \text{QuantumGroups$\grave{ }$a}^6 z^6+152 \text{QuantumGroups$\grave{ }$a}^4 z^6+74 \text{QuantumGroups$\grave{ }$a}^2 z^6+z^6 $Failed^{-1} -17 z^6+11 \text{QuantumGroups$\grave{ }$a}^{11} z^5-13 \text{QuantumGroups$\grave{ }$a}^9 z^5-66 \text{QuantumGroups$\grave{ }$a}^7 z^5-73 \text{QuantumGroups$\grave{ }$a}^5 z^5+8 \text{QuantumGroups$\grave{ }$a}^3 z^5+34 \text{QuantumGroups$\grave{ }$a} z^5-5 z^5 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^{12} z^4-15 \text{QuantumGroups$\grave{ }$a}^{10} z^4-18 \text{QuantumGroups$\grave{ }$a}^8 z^4-33 \text{QuantumGroups$\grave{ }$a}^6 z^4-73 \text{QuantumGroups$\grave{ }$a}^4 z^4-33 \text{QuantumGroups$\grave{ }$a}^2 z^4-z^4 $Failed^{-1} +8 z^4-3 \text{QuantumGroups$\grave{ }$a}^{11} z^3+5 \text{QuantumGroups$\grave{ }$a}^9 z^3+26 \text{QuantumGroups$\grave{ }$a}^7 z^3+23 \text{QuantumGroups$\grave{ }$a}^5 z^3-5 \text{QuantumGroups$\grave{ }$a}^3 z^3-9 \text{QuantumGroups$\grave{ }$a} z^3+z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^{10} z^2+\text{QuantumGroups$\grave{ }$a}^8 z^2+2 \text{QuantumGroups$\grave{ }$a}^6 z^2+9 \text{QuantumGroups$\grave{ }$a}^4 z^2+6 \text{QuantumGroups$\grave{ }$a}^2 z^2-z^2-\text{QuantumGroups$\grave{ }$a}^9 z-7 \text{QuantumGroups$\grave{ }$a}^7 z-8 \text{QuantumGroups$\grave{ }$a}^5 z-2 \text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a}^6+3 \text{QuantumGroups$\grave{ }$a}^4}

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