K14a7648

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a7648

Polynomial invariants

Jones polynomial	Data:K14a7648/Jones Polynomial
Alexander polynomial	$2t^{4}-19t^{3}+69t^{2}-138t+173-138t^{-1}+69t^{-2}-19t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a7648/Conway Polynomial
Determinant	Data:K14a7648/Determinant
Signature	Data:K14a7648/Signature
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}-2a^{2}z^{6}-2z^{6}a^{-4}+z^{6}+a^{4}z^{4}-3a^{2}z^{4}-4z^{4}a^{-2}-2z^{4}a^{-4}+z^{4}a^{-6}+2z^{4}+a^{4}z^{2}-2a^{2}z^{2}-6z^{2}a^{-2}+z^{2}a^{-4}+z^{2}a^{-6}+4z^{2}-2a^{-2}+a^{-4}+2$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 3 z^{13} $Failed^{-1} +3 z^{13} $Failed^{-1} +24 z^{12} $Failed^{-1} +11 z^{12} $Failed^{-1} +13 z^{12}+25 \text{QuantumGroups$\grave{ }$a} z^{11}+49 z^{11} $Failed^{-1} +40 z^{11} $Failed^{-1} +16 z^{11} $Failed^{-1} +29 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-3 z^{10} $Failed^{-1} +6 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} +32 z^{10}+23 \text{QuantumGroups$\grave{ }$a}^3 z^9-15 \text{QuantumGroups$\grave{ }$a} z^9-112 z^9 $Failed^{-1} -115 z^9 $Failed^{-1} -36 z^9 $Failed^{-1} +5 z^9 $Failed^{-1} +13 \text{QuantumGroups$\grave{ }$a}^4 z^8-41 \text{QuantumGroups$\grave{ }$a}^2 z^8-118 z^8 $Failed^{-1} -84 z^8 $Failed^{-1} -35 z^8 $Failed^{-1} +z^8 $Failed^{-1} -124 z^8+5 \text{QuantumGroups$\grave{ }$a}^5 z^7-35 \text{QuantumGroups$\grave{ }$a}^3 z^7-43 \text{QuantumGroups$\grave{ }$a} z^7+48 z^7 $Failed^{-1} +81 z^7 $Failed^{-1} +15 z^7 $Failed^{-1} -15 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^6 z^6-18 \text{QuantumGroups$\grave{ }$a}^4 z^6+16 \text{QuantumGroups$\grave{ }$a}^2 z^6+140 z^6 $Failed^{-1} +104 z^6 $Failed^{-1} +36 z^6 $Failed^{-1} -3 z^6 $Failed^{-1} +110 z^6-6 \text{QuantumGroups$\grave{ }$a}^5 z^5+24 \text{QuantumGroups$\grave{ }$a}^3 z^5+57 \text{QuantumGroups$\grave{ }$a} z^5+26 z^5 $Failed^{-1} -7 z^5 $Failed^{-1} +10 z^5 $Failed^{-1} +16 z^5 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^6 z^4+11 \text{QuantumGroups$\grave{ }$a}^4 z^4+7 \text{QuantumGroups$\grave{ }$a}^2 z^4-51 z^4 $Failed^{-1} -46 z^4 $Failed^{-1} -17 z^4 $Failed^{-1} +3 z^4 $Failed^{-1} -30 z^4+2 \text{QuantumGroups$\grave{ }$a}^5 z^3-7 \text{QuantumGroups$\grave{ }$a}^3 z^3-23 \text{QuantumGroups$\grave{ }$a} z^3-24 z^3 $Failed^{-1} -10 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} -7 z^3 $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4 z^2-4 \text{QuantumGroups$\grave{ }$a}^2 z^2-z^2 $Failed^{-1} +6 z^2 $Failed^{-1} +4 z^2 $Failed^{-1} -z^2 $Failed^{-1} -3 z^2+\text{QuantumGroups$\grave{ }$a}^3 z+3 \text{QuantumGroups$\grave{ }$a} z+4 z $Failed^{-1} +3 z $Failed^{-1} +2 z $Failed^{-1} +z $Failed^{-1} +2 $Failed^{-1} + $Failed^{-1} +2}

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