K14a7085

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a7085

Polynomial invariants

Jones polynomial	Data:K14a7085/Jones Polynomial
Alexander polynomial	$2t^{4}-14t^{3}+43t^{2}-78t+95-78t^{-1}+43t^{-2}-14t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a7085/Conway Polynomial
Determinant	Data:K14a7085/Determinant
Signature	Data:K14a7085/Signature
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}-2a^{2}z^{6}+3z^{6}a^{-2}-2z^{6}a^{-4}+3z^{6}+a^{4}z^{4}-6a^{2}z^{4}+5z^{4}a^{-2}-6z^{4}a^{-4}+z^{4}a^{-6}+4z^{4}+2a^{4}z^{2}-6a^{2}z^{2}+7z^{2}a^{-2}-6z^{2}a^{-4}+2z^{2}a^{-6}+z^{2}+a^{4}-a^{2}+5a^{-2}-2a^{-4}-2$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle z^{13} $Failed^{-1} +z^{13} $Failed^{-1} +8 z^{12} $Failed^{-1} +4 z^{12} $Failed^{-1} +4 z^{12}+8 \text{QuantumGroups$\grave{ }$a} z^{11}+15 z^{11} $Failed^{-1} +14 z^{11} $Failed^{-1} +7 z^{11} $Failed^{-1} +11 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-3 z^{10} $Failed^{-1} +3 z^{10} $Failed^{-1} +7 z^{10} $Failed^{-1} +12 z^{10}+11 \text{QuantumGroups$\grave{ }$a}^3 z^9+\text{QuantumGroups$\grave{ }$a} z^9-32 z^9 $Failed^{-1} -44 z^9 $Failed^{-1} -18 z^9 $Failed^{-1} +4 z^9 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^4 z^8-13 \text{QuantumGroups$\grave{ }$a}^2 z^8-34 z^8 $Failed^{-1} -43 z^8 $Failed^{-1} -27 z^8 $Failed^{-1} +z^8 $Failed^{-1} -40 z^8+4 \text{QuantumGroups$\grave{ }$a}^5 z^7-19 \text{QuantumGroups$\grave{ }$a}^3 z^7-30 \text{QuantumGroups$\grave{ }$a} z^7+13 z^7 $Failed^{-1} +40 z^7 $Failed^{-1} +3 z^7 $Failed^{-1} -17 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^6-15 \text{QuantumGroups$\grave{ }$a}^4 z^6-\text{QuantumGroups$\grave{ }$a}^2 z^6+54 z^6 $Failed^{-1} +71 z^6 $Failed^{-1} +35 z^6 $Failed^{-1} -4 z^6 $Failed^{-1} +37 z^6-8 \text{QuantumGroups$\grave{ }$a}^5 z^5+14 \text{QuantumGroups$\grave{ }$a}^3 z^5+44 \text{QuantumGroups$\grave{ }$a} z^5+9 z^5 $Failed^{-1} -16 z^5 $Failed^{-1} +20 z^5 $Failed^{-1} +23 z^5 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^4+9 \text{QuantumGroups$\grave{ }$a}^4 z^4+11 \text{QuantumGroups$\grave{ }$a}^2 z^4-47 z^4 $Failed^{-1} -61 z^4 $Failed^{-1} -21 z^4 $Failed^{-1} +4 z^4 $Failed^{-1} -11 z^4+4 \text{QuantumGroups$\grave{ }$a}^5 z^3-9 \text{QuantumGroups$\grave{ }$a}^3 z^3-24 \text{QuantumGroups$\grave{ }$a} z^3-4 z^3 $Failed^{-1} -17 z^3 $Failed^{-1} -10 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^2-3 \text{QuantumGroups$\grave{ }$a}^4 z^2-8 \text{QuantumGroups$\grave{ }$a}^2 z^2+27 z^2 $Failed^{-1} +25 z^2 $Failed^{-1} +7 z^2 $Failed^{-1} +5 z^2+3 \text{QuantumGroups$\grave{ }$a}^3 z+4 \text{QuantumGroups$\grave{ }$a} z+z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4+\text{QuantumGroups$\grave{ }$a}^2-5 $Failed^{-1} -2 $Failed^{-1} -2}

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