K14a5709

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a5709

Polynomial invariants

Jones polynomial	Data:K14a5709/Jones Polynomial
Alexander polynomial	$t^{5}-9t^{4}+34t^{3}-76t^{2}+119t-137+119t^{-1}-76t^{-2}+34t^{-3}-9t^{-4}+t^{-5}$
Conway polynomial	Data:K14a5709/Conway Polynomial
Determinant	Data:K14a5709/Determinant
Signature	Data:K14a5709/Signature
HOMFLY-PT polynomial	$z^{10}a^{-2}+5z^{8}a^{-2}-2z^{8}a^{-4}-2z^{8}+a^{2}z^{6}+11z^{6}a^{-2}-8z^{6}a^{-4}+z^{6}a^{-6}-8z^{6}+3a^{2}z^{4}+15z^{4}a^{-2}-11z^{4}a^{-4}+3z^{4}a^{-6}-12z^{4}+3a^{2}z^{2}+14z^{2}a^{-2}-7z^{2}a^{-4}+2z^{2}a^{-6}-10z^{2}+a^{2}+7a^{-2}-3a^{-4}-4$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 3 z^{13} $Failed^{-1} +3 z^{13} $Failed^{-1} +24 z^{12} $Failed^{-1} +13 z^{12} $Failed^{-1} +11 z^{12}+16 \text{QuantumGroups$\grave{ }$a} z^{11}+39 z^{11} $Failed^{-1} +48 z^{11} $Failed^{-1} +25 z^{11} $Failed^{-1} +12 \text{QuantumGroups$\grave{ }$a}^2 z^{10}-9 z^{10} $Failed^{-1} +28 z^{10} $Failed^{-1} +29 z^{10} $Failed^{-1} +4 z^{10}+5 \text{QuantumGroups$\grave{ }$a}^3 z^9-37 \text{QuantumGroups$\grave{ }$a} z^9-119 z^9 $Failed^{-1} -122 z^9 $Failed^{-1} -22 z^9 $Failed^{-1} +23 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^8-35 \text{QuantumGroups$\grave{ }$a}^2 z^8-109 z^8 $Failed^{-1} -125 z^8 $Failed^{-1} -47 z^8 $Failed^{-1} +13 z^8 $Failed^{-1} -80 z^8-15 \text{QuantumGroups$\grave{ }$a}^3 z^7+17 \text{QuantumGroups$\grave{ }$a} z^7+99 z^7 $Failed^{-1} +82 z^7 $Failed^{-1} -27 z^7 $Failed^{-1} -37 z^7 $Failed^{-1} +5 z^7 $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4 z^6+35 \text{QuantumGroups$\grave{ }$a}^2 z^6+151 z^6 $Failed^{-1} +138 z^6 $Failed^{-1} +32 z^6 $Failed^{-1} -18 z^6 $Failed^{-1} +z^6 $Failed^{-1} +102 z^6+16 \text{QuantumGroups$\grave{ }$a}^3 z^5+6 \text{QuantumGroups$\grave{ }$a} z^5-32 z^5 $Failed^{-1} -8 z^5 $Failed^{-1} +46 z^5 $Failed^{-1} +26 z^5 $Failed^{-1} -6 z^5 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^4 z^4-16 \text{QuantumGroups$\grave{ }$a}^2 z^4-81 z^4 $Failed^{-1} -69 z^4 $Failed^{-1} -12 z^4 $Failed^{-1} +9 z^4 $Failed^{-1} -z^4 $Failed^{-1} -53 z^4-7 \text{QuantumGroups$\grave{ }$a}^3 z^3-5 \text{QuantumGroups$\grave{ }$a} z^3+5 z^3 $Failed^{-1} -9 z^3 $Failed^{-1} -22 z^3 $Failed^{-1} -8 z^3 $Failed^{-1} +2 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^4 z^2+4 \text{QuantumGroups$\grave{ }$a}^2 z^2+26 z^2 $Failed^{-1} +18 z^2 $Failed^{-1} +3 z^2 $Failed^{-1} -z^2 $Failed^{-1} +17 z^2+\text{QuantumGroups$\grave{ }$a}^3 z+2 \text{QuantumGroups$\grave{ }$a} z+2 z $Failed^{-1} +4 z $Failed^{-1} +3 z $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^2-7 $Failed^{-1} -3 $Failed^{-1} -4}

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