K14a18491

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a18491

Polynomial invariants

Jones polynomial	Data:K14a18491/Jones Polynomial
Alexander polynomial	$4t^{4}-24t^{3}+66t^{2}-114t+137-114t^{-1}+66t^{-2}-24t^{-3}+4t^{-4}$
Conway polynomial	Data:K14a18491/Conway Polynomial
Determinant	Data:K14a18491/Determinant
Signature	Data:K14a18491/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}a^{-2}+2z^{8}-a^{4}z^{6}+a^{2}z^{6}+3z^{6}a^{-2}-z^{6}a^{-4}+6z^{6}-a^{4}z^{4}-3a^{2}z^{4}+4z^{4}a^{-2}-3z^{4}a^{-4}+5z^{4}+a^{4}z^{2}-4a^{2}z^{2}+3z^{2}a^{-2}-2z^{2}a^{-4}+a^{4}-a^{2}+a^{-2}$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 4 \text{QuantumGroups$\grave{ }$a} z^{13}+4 z^{13} $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+11 z^{12} $Failed^{-1} +25 z^{12}+24 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+30 \text{QuantumGroups$\grave{ }$a} z^{11}+20 z^{11} $Failed^{-1} +14 z^{11} $Failed^{-1} +25 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-2 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-17 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} -56 z^{10}+16 \text{QuantumGroups$\grave{ }$a}^5 z^9-44 \text{QuantumGroups$\grave{ }$a}^3 z^9-96 \text{QuantumGroups$\grave{ }$a} z^9-79 z^9 $Failed^{-1} -35 z^9 $Failed^{-1} +8 z^9 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^6 z^8-56 \text{QuantumGroups$\grave{ }$a}^4 z^8-52 \text{QuantumGroups$\grave{ }$a}^2 z^8+7 z^8 $Failed^{-1} -30 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} +51 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-33 \text{QuantumGroups$\grave{ }$a}^5 z^7+11 \text{QuantumGroups$\grave{ }$a}^3 z^7+100 \text{QuantumGroups$\grave{ }$a} z^7+120 z^7 $Failed^{-1} +43 z^7 $Failed^{-1} -21 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+35 \text{QuantumGroups$\grave{ }$a}^4 z^6+51 \text{QuantumGroups$\grave{ }$a}^2 z^6+12 z^6 $Failed^{-1} +27 z^6 $Failed^{-1} -12 z^6 $Failed^{-1} -21 z^6-\text{QuantumGroups$\grave{ }$a}^7 z^5+16 \text{QuantumGroups$\grave{ }$a}^5 z^5+7 \text{QuantumGroups$\grave{ }$a}^3 z^5-44 \text{QuantumGroups$\grave{ }$a} z^5-81 z^5 $Failed^{-1} -28 z^5 $Failed^{-1} +16 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^6 z^4-10 \text{QuantumGroups$\grave{ }$a}^4 z^4-11 \text{QuantumGroups$\grave{ }$a}^2 z^4-11 z^4 $Failed^{-1} -10 z^4 $Failed^{-1} +10 z^4 $Failed^{-1} +11 z^4-\text{QuantumGroups$\grave{ }$a}^5 z^3-6 \text{QuantumGroups$\grave{ }$a}^3 z^3+10 \text{QuantumGroups$\grave{ }$a} z^3+27 z^3 $Failed^{-1} +6 z^3 $Failed^{-1} -4 z^3 $Failed^{-1} +2 z^3 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^2-\text{QuantumGroups$\grave{ }$a}^4 z^2-5 \text{QuantumGroups$\grave{ }$a}^2 z^2+3 z^2 $Failed^{-1} -z^2 $Failed^{-1} -2 z^2 $Failed^{-1} -z^2+\text{QuantumGroups$\grave{ }$a}^3 z-\text{QuantumGroups$\grave{ }$a} z-3 z $Failed^{-1} -z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4+\text{QuantumGroups$\grave{ }$a}^2- $Failed^{-1} }

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