K14a861

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a861

Polynomial invariants

Jones polynomial	Data:K14a861/Jones Polynomial
Alexander polynomial	$t^{5}-8t^{4}+31t^{3}-75t^{2}+124t-145+124t^{-1}-75t^{-2}+31t^{-3}-8t^{-4}+t^{-5}$
Conway polynomial	Data:K14a861/Conway Polynomial
Determinant	Data:K14a861/Determinant
Signature	Data:K14a861/Signature
HOMFLY-PT polynomial	$a^{2}z^{10}-2a^{4}z^{8}+6a^{2}z^{8}-2z^{8}+a^{6}z^{6}-9a^{4}z^{6}+17a^{2}z^{6}+z^{6}a^{-2}-8z^{6}+3a^{6}z^{4}-17a^{4}z^{4}+24a^{2}z^{4}+2z^{4}a^{-2}-11z^{4}+4a^{6}z^{2}-15a^{4}z^{2}+15a^{2}z^{2}-4z^{2}+2a^{6}-5a^{4}+3a^{2}-a^{-2}+2$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+2 \text{QuantumGroups$\grave{ }$a} z^{13}+11 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+20 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+9 z^{12}+24 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+53 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+45 \text{QuantumGroups$\grave{ }$a} z^{11}+16 z^{11} $Failed^{-1} +30 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+44 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+24 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+14 z^{10} $Failed^{-1} +24 z^{10}+25 \text{QuantumGroups$\grave{ }$a}^7 z^9-10 \text{QuantumGroups$\grave{ }$a}^5 z^9-120 \text{QuantumGroups$\grave{ }$a}^3 z^9-121 \text{QuantumGroups$\grave{ }$a} z^9-30 z^9 $Failed^{-1} +6 z^9 $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^8 z^8-45 \text{QuantumGroups$\grave{ }$a}^6 z^8-160 \text{QuantumGroups$\grave{ }$a}^4 z^8-200 \text{QuantumGroups$\grave{ }$a}^2 z^8-42 z^8 $Failed^{-1} +z^8 $Failed^{-1} -142 z^8+5 \text{QuantumGroups$\grave{ }$a}^9 z^7-42 \text{QuantumGroups$\grave{ }$a}^7 z^7-51 \text{QuantumGroups$\grave{ }$a}^5 z^7+60 \text{QuantumGroups$\grave{ }$a}^3 z^7+70 \text{QuantumGroups$\grave{ }$a} z^7-11 z^7 $Failed^{-1} -17 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^{10} z^6-20 \text{QuantumGroups$\grave{ }$a}^8 z^6+25 \text{QuantumGroups$\grave{ }$a}^6 z^6+178 \text{QuantumGroups$\grave{ }$a}^4 z^6+272 \text{QuantumGroups$\grave{ }$a}^2 z^6+42 z^6 $Failed^{-1} -2 z^6 $Failed^{-1} +184 z^6-5 \text{QuantumGroups$\grave{ }$a}^9 z^5+34 \text{QuantumGroups$\grave{ }$a}^7 z^5+60 \text{QuantumGroups$\grave{ }$a}^5 z^5+11 \text{QuantumGroups$\grave{ }$a}^3 z^5+16 \text{QuantumGroups$\grave{ }$a} z^5+41 z^5 $Failed^{-1} +15 z^5 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^{10} z^4+13 \text{QuantumGroups$\grave{ }$a}^8 z^4-9 \text{QuantumGroups$\grave{ }$a}^6 z^4-107 \text{QuantumGroups$\grave{ }$a}^4 z^4-162 \text{QuantumGroups$\grave{ }$a}^2 z^4-16 z^4 $Failed^{-1} +z^4 $Failed^{-1} -95 z^4+\text{QuantumGroups$\grave{ }$a}^9 z^3-15 \text{QuantumGroups$\grave{ }$a}^7 z^3-25 \text{QuantumGroups$\grave{ }$a}^5 z^3-10 \text{QuantumGroups$\grave{ }$a}^3 z^3-12 \text{QuantumGroups$\grave{ }$a} z^3-14 z^3 $Failed^{-1} -3 z^3 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^8 z^2+6 \text{QuantumGroups$\grave{ }$a}^6 z^2+37 \text{QuantumGroups$\grave{ }$a}^4 z^2+44 \text{QuantumGroups$\grave{ }$a}^2 z^2+z^2 $Failed^{-1} +18 z^2+3 \text{QuantumGroups$\grave{ }$a}^7 z+4 \text{QuantumGroups$\grave{ }$a}^5 z-\text{QuantumGroups$\grave{ }$a}^3 z-3 \text{QuantumGroups$\grave{ }$a} z-2 z $Failed^{-1} -z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6-5 \text{QuantumGroups$\grave{ }$a}^4-3 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +2}

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