K12a1063
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Polynomial invariants
| Jones polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^8-3 q^7+6 q^6-9 q^5+12 q^4-15 q^3+16 q^2-15 q+13-9 q^{-1} +6 q^{-2} -3 q^{-3} + q^{-4} } |
| Alexander polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 t^3+12 t^2-24 t+31-24 t^{-1} +12 t^{-2} -3 t^{-3} } |
| Conway polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 z^6-6 z^4-3 z^2+1} |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-2 z^4 a^{-2} -3 z^4 a^{-4} +z^4 a^{-6} -3 z^4+2 a^2 z^2-z^2 a^{-2} -3 z^2 a^{-4} +2 z^2 a^{-6} -3 z^2+a^2- a^{-4} + a^{-6} } |
| Kauffman polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +9 z^{10} a^{-4} +4 z^{10} a^{-6} +6 z^9 a^{-1} -3 z^9 a^{-5} +3 z^9 a^{-7} -16 z^8 a^{-2} -42 z^8 a^{-4} -19 z^8 a^{-6} +z^8 a^{-8} +6 z^8+6 a z^7-15 z^7 a^{-1} -24 z^7 a^{-3} -18 z^7 a^{-5} -15 z^7 a^{-7} +5 a^2 z^6+19 z^6 a^{-2} +64 z^6 a^{-4} +26 z^6 a^{-6} -5 z^6 a^{-8} -9 z^6+3 a^3 z^5-8 a z^5+15 z^5 a^{-1} +44 z^5 a^{-3} +40 z^5 a^{-5} +22 z^5 a^{-7} +a^4 z^4-6 a^2 z^4-13 z^4 a^{-2} -43 z^4 a^{-4} -14 z^4 a^{-6} +7 z^4 a^{-8} +2 z^4-3 a^3 z^3+4 a z^3-10 z^3 a^{-1} -31 z^3 a^{-3} -26 z^3 a^{-5} -12 z^3 a^{-7} -a^4 z^2+3 a^2 z^2+2 z^2 a^{-2} +12 z^2 a^{-4} +6 z^2 a^{-6} -3 z^2 a^{-8} +3 z^2+3 z a^{-1} +6 z a^{-3} +6 z a^{-5} +3 z a^{-7} -a^2- a^{-4} - a^{-6} } |
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