K14a2076

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a2076

Polynomial invariants

Jones polynomial	Data:K14a2076/Jones Polynomial
Alexander polynomial	$t^{4}-13t^{3}+58t^{2}-132t+173-132t^{-1}+58t^{-2}-13t^{-3}+t^{-4}$
Conway polynomial	Data:K14a2076/Conway Polynomial
Determinant	Data:K14a2076/Determinant
Signature	Data:K14a2076/Signature
HOMFLY-PT polynomial	$z^{8}-3a^{2}z^{6}-3z^{6}a^{-2}+z^{6}+3a^{4}z^{4}-4a^{2}z^{4}-3z^{4}a^{-2}+3z^{4}a^{-4}+z^{4}-a^{6}z^{2}+4a^{4}z^{2}-2a^{2}z^{2}+2z^{2}a^{-4}-z^{2}a^{-6}-3z^{2}-a^{6}+2a^{4}+a^{2}+2a^{-2}-3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+9 z^{12} $Failed^{-1} +17 z^{12}+14 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+35 \text{QuantumGroups$\grave{ }$a} z^{11}+38 z^{11} $Failed^{-1} +17 z^{11} $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+23 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+26 z^{10} $Failed^{-1} +18 z^{10} $Failed^{-1} +17 z^{10}+9 \text{QuantumGroups$\grave{ }$a}^5 z^9-11 \text{QuantumGroups$\grave{ }$a}^3 z^9-69 \text{QuantumGroups$\grave{ }$a} z^9-75 z^9 $Failed^{-1} -14 z^9 $Failed^{-1} +12 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-26 \text{QuantumGroups$\grave{ }$a}^4 z^8-89 \text{QuantumGroups$\grave{ }$a}^2 z^8-100 z^8 $Failed^{-1} -34 z^8 $Failed^{-1} +5 z^8 $Failed^{-1} -120 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-19 \text{QuantumGroups$\grave{ }$a}^5 z^7-21 \text{QuantumGroups$\grave{ }$a}^3 z^7+25 \text{QuantumGroups$\grave{ }$a} z^7+24 z^7 $Failed^{-1} -29 z^7 $Failed^{-1} -26 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+18 \text{QuantumGroups$\grave{ }$a}^4 z^6+106 \text{QuantumGroups$\grave{ }$a}^2 z^6+105 z^6 $Failed^{-1} +19 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +153 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+14 \text{QuantumGroups$\grave{ }$a}^5 z^5+36 \text{QuantumGroups$\grave{ }$a}^3 z^5+25 \text{QuantumGroups$\grave{ }$a} z^5+27 z^5 $Failed^{-1} +43 z^5 $Failed^{-1} +20 z^5 $Failed^{-1} -2 z^5 $Failed^{-1} +9 \text{QuantumGroups$\grave{ }$a}^6 z^4-5 \text{QuantumGroups$\grave{ }$a}^4 z^4-63 \text{QuantumGroups$\grave{ }$a}^2 z^4-54 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} +8 z^4 $Failed^{-1} -93 z^4+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-4 \text{QuantumGroups$\grave{ }$a}^5 z^3-20 \text{QuantumGroups$\grave{ }$a}^3 z^3-21 \text{QuantumGroups$\grave{ }$a} z^3-21 z^3 $Failed^{-1} -21 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} +z^3 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^6 z^2-2 \text{QuantumGroups$\grave{ }$a}^4 z^2+17 \text{QuantumGroups$\grave{ }$a}^2 z^2+15 z^2 $Failed^{-1} -z^2 $Failed^{-1} -2 z^2 $Failed^{-1} +29 z^2-\text{QuantumGroups$\grave{ }$a}^7 z+3 \text{QuantumGroups$\grave{ }$a}^3 z+3 \text{QuantumGroups$\grave{ }$a} z+4 z $Failed^{-1} +4 z $Failed^{-1} +z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6+2 \text{QuantumGroups$\grave{ }$a}^4-\text{QuantumGroups$\grave{ }$a}^2-2 $Failed^{-1} -3}

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