K14a9

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a9

Polynomial invariants

Jones polynomial	Data:K14a9/Jones Polynomial
Alexander polynomial	$-t^{5}+7t^{4}-21t^{3}+36t^{2}-42t+43-42t^{-1}+36t^{-2}-21t^{-3}+7t^{-4}-t^{-5}$
Conway polynomial	Data:K14a9/Conway Polynomial
Determinant	Data:K14a9/Determinant
Signature	Data:K14a9/Signature
HOMFLY-PT polynomial	$-z^{10}a^{-4}+3z^{8}a^{-2}-7z^{8}a^{-4}+z^{8}a^{-6}+18z^{6}a^{-2}-20z^{6}a^{-4}+5z^{6}a^{-6}-3z^{6}+a^{2}z^{4}+37z^{4}a^{-2}-31z^{4}a^{-4}+8z^{4}a^{-6}-15z^{4}+4a^{2}z^{2}+34z^{2}a^{-2}-23z^{2}a^{-4}+6z^{2}a^{-6}-21z^{2}+3a^{2}+12a^{-2}-6a^{-4}+a^{-6}-9$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle z^{13} $Failed^{-1} +z^{13} $Failed^{-1} +9 z^{12} $Failed^{-1} +6 z^{12} $Failed^{-1} +3 z^{12}+3 \text{QuantumGroups$\grave{ }$a} z^{11}+9 z^{11} $Failed^{-1} +20 z^{11} $Failed^{-1} +14 z^{11} $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^2 z^{10}-31 z^{10} $Failed^{-1} +z^{10} $Failed^{-1} +19 z^{10} $Failed^{-1} -12 z^{10}-20 \text{QuantumGroups$\grave{ }$a} z^9-79 z^9 $Failed^{-1} -119 z^9 $Failed^{-1} -40 z^9 $Failed^{-1} +20 z^9 $Failed^{-1} -7 \text{QuantumGroups$\grave{ }$a}^2 z^8-20 z^8 $Failed^{-1} -94 z^8 $Failed^{-1} -52 z^8 $Failed^{-1} +19 z^8 $Failed^{-1} -4 z^8+48 \text{QuantumGroups$\grave{ }$a} z^7+182 z^7 $Failed^{-1} +207 z^7 $Failed^{-1} +17 z^7 $Failed^{-1} -41 z^7 $Failed^{-1} +15 z^7 $Failed^{-1} +18 \text{QuantumGroups$\grave{ }$a}^2 z^6+163 z^6 $Failed^{-1} +190 z^6 $Failed^{-1} +36 z^6 $Failed^{-1} -32 z^6 $Failed^{-1} +9 z^6 $Failed^{-1} +68 z^6-53 \text{QuantumGroups$\grave{ }$a} z^5-172 z^5 $Failed^{-1} -145 z^5 $Failed^{-1} +8 z^5 $Failed^{-1} +11 z^5 $Failed^{-1} -19 z^5 $Failed^{-1} +4 z^5 $Failed^{-1} -22 \text{QuantumGroups$\grave{ }$a}^2 z^4-189 z^4 $Failed^{-1} -146 z^4 $Failed^{-1} -16 z^4 $Failed^{-1} +11 z^4 $Failed^{-1} -6 z^4 $Failed^{-1} +z^4 $Failed^{-1} -99 z^4+27 \text{QuantumGroups$\grave{ }$a} z^3+70 z^3 $Failed^{-1} +48 z^3 $Failed^{-1} +3 z^3 $Failed^{-1} +6 z^3 $Failed^{-1} +7 z^3 $Failed^{-1} -z^3 $Failed^{-1} +13 \text{QuantumGroups$\grave{ }$a}^2 z^2+82 z^2 $Failed^{-1} +52 z^2 $Failed^{-1} +8 z^2 $Failed^{-1} -z^2 $Failed^{-1} +z^2 $Failed^{-1} +53 z^2-5 \text{QuantumGroups$\grave{ }$a} z-11 z $Failed^{-1} -8 z $Failed^{-1} -4 z $Failed^{-1} -3 z $Failed^{-1} -z $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^2-12 $Failed^{-1} -6 $Failed^{-1} - $Failed^{-1} -9}

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