K12a1040
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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^5-2 q^4+5 q^3-8 q^2+12 q-16+17 q^{-1} -17 q^{-2} +15 q^{-3} -11 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} } |
| 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 2 t^3-13 t^2+27 t-31+27 t^{-1} -13 t^{-2} +2 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 2 z^6-z^4-7 z^2+1} |
| Determinant | 115 |
| Signature | -2 |
| 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^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4+z^6 a^2+z^4 a^2-2 z^2 a^2-a^2+z^6+2 z^4+z^2+1-2 z^4 a^{-2} -5 z^2 a^{-2} -2 a^{-2} +z^2 a^{-4} +2 a^{-4} } |
| 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 a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+2 z^{10} a^{-2} +5 z^{10}+6 a^3 z^9+4 a z^9+2 z^9 a^{-3} +8 a^4 z^8-7 z^8 a^{-2} +z^8 a^{-4} -16 z^8+8 a^5 z^7-9 a^3 z^7-16 a z^7-9 z^7 a^{-1} -10 z^7 a^{-3} +6 a^6 z^6-12 a^4 z^6-11 a^2 z^6+3 z^6 a^{-2} -6 z^6 a^{-4} +16 z^6+3 a^7 z^5-11 a^5 z^5+6 a^3 z^5+13 a z^5+8 z^5 a^{-1} +15 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+6 a^4 z^4+7 a^2 z^4+8 z^4 a^{-2} +12 z^4 a^{-4} -11 z^4-2 a^7 z^3+7 a^5 z^3-9 a^3 z^3-8 a z^3+4 z^3 a^{-1} -6 z^3 a^{-3} -a^8 z^2+5 a^6 z^2-5 a^2 z^2-6 z^2 a^{-2} -9 z^2 a^{-4} +4 z^2+4 a^3 z+a z-3 z a^{-1} -a^6+a^2+2 a^{-2} +2 a^{-4} +1} |
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