K14a48

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a48

Polynomial invariants

Jones polynomial	Data:K14a48/Jones Polynomial
Alexander polynomial	$2t^{4}-15t^{3}+51t^{2}-104t+133-104t^{-1}+51t^{-2}-15t^{-3}+2t^{-4}$
Conway polynomial	Data:K14a48/Conway Polynomial
Determinant	Data:K14a48/Determinant
Signature	Data:K14a48/Signature
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}-2a^{4}z^{6}+3a^{2}z^{6}-2z^{6}a^{-2}+2z^{6}+a^{6}z^{4}-6a^{4}z^{4}+8a^{2}z^{4}-5z^{4}a^{-2}+z^{4}a^{-4}+2z^{4}+2a^{6}z^{2}-10a^{4}z^{2}+10a^{2}z^{2}-6z^{2}a^{-2}+2z^{2}a^{-4}-z^{2}+2a^{6}-5a^{4}+5a^{2}-a^{-2}+a^{-4}-1$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle \text{QuantumGroups$\grave{ }$a}^3 z^{13}+\text{QuantumGroups$\grave{ }$a} z^{13}+5 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+11 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+6 z^{12}+9 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+27 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+32 \text{QuantumGroups$\grave{ }$a} z^{11}+14 z^{11} $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+14 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+19 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+18 z^{10} $Failed^{-1} +31 z^{10}+4 \text{QuantumGroups$\grave{ }$a}^7 z^9-19 \text{QuantumGroups$\grave{ }$a}^5 z^9-75 \text{QuantumGroups$\grave{ }$a}^3 z^9-69 \text{QuantumGroups$\grave{ }$a} z^9-2 z^9 $Failed^{-1} +15 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^8 z^8-27 \text{QuantumGroups$\grave{ }$a}^6 z^8-87 \text{QuantumGroups$\grave{ }$a}^4 z^8-131 \text{QuantumGroups$\grave{ }$a}^2 z^8-26 z^8 $Failed^{-1} +9 z^8 $Failed^{-1} -107 z^8-15 \text{QuantumGroups$\grave{ }$a}^7 z^7-2 \text{QuantumGroups$\grave{ }$a}^5 z^7+55 \text{QuantumGroups$\grave{ }$a}^3 z^7+30 \text{QuantumGroups$\grave{ }$a} z^7-40 z^7 $Failed^{-1} -24 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -4 \text{QuantumGroups$\grave{ }$a}^8 z^6+32 \text{QuantumGroups$\grave{ }$a}^6 z^6+131 \text{QuantumGroups$\grave{ }$a}^4 z^6+189 \text{QuantumGroups$\grave{ }$a}^2 z^6+13 z^6 $Failed^{-1} -14 z^6 $Failed^{-1} +z^6 $Failed^{-1} +122 z^6+19 \text{QuantumGroups$\grave{ }$a}^7 z^5+24 \text{QuantumGroups$\grave{ }$a}^5 z^5-4 \text{QuantumGroups$\grave{ }$a}^3 z^5+17 \text{QuantumGroups$\grave{ }$a} z^5+50 z^5 $Failed^{-1} +17 z^5 $Failed^{-1} -7 z^5 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^8 z^4-20 \text{QuantumGroups$\grave{ }$a}^6 z^4-96 \text{QuantumGroups$\grave{ }$a}^4 z^4-131 \text{QuantumGroups$\grave{ }$a}^2 z^4+5 z^4 $Failed^{-1} +9 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -66 z^4-10 \text{QuantumGroups$\grave{ }$a}^7 z^3-16 \text{QuantumGroups$\grave{ }$a}^5 z^3-11 \text{QuantumGroups$\grave{ }$a}^3 z^3-16 \text{QuantumGroups$\grave{ }$a} z^3-18 z^3 $Failed^{-1} -3 z^3 $Failed^{-1} +4 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^8 z^2+9 \text{QuantumGroups$\grave{ }$a}^6 z^2+36 \text{QuantumGroups$\grave{ }$a}^4 z^2+43 \text{QuantumGroups$\grave{ }$a}^2 z^2-7 z^2 $Failed^{-1} -4 z^2 $Failed^{-1} +z^2 $Failed^{-1} +16 z^2+2 \text{QuantumGroups$\grave{ }$a}^7 z+3 \text{QuantumGroups$\grave{ }$a}^5 z+3 \text{QuantumGroups$\grave{ }$a}^3 z+3 \text{QuantumGroups$\grave{ }$a} z+z $Failed^{-1} -z $Failed^{-1} -z $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6-5 \text{QuantumGroups$\grave{ }$a}^4-5 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} + $Failed^{-1} -1}

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