K12a1015
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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^5-3 q^4+6 q^3-10 q^2+15 q-18+20 q^{-1} -19 q^{-2} +16 q^{-3} -12 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^4+8 t^3-17 t^2+25 t-27+25 t^{-1} -17 t^{-2} +8 t^{-3} -2 t^{-4} } |
| 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^8-8 z^6-9 z^4-3 z^2+1} |
| Determinant | 131 |
| 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 -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -5 z^6+4 a^4 z^4-9 a^2 z^4+4 z^4 a^{-2} -8 z^4+5 a^4 z^2-8 a^2 z^2+4 z^2 a^{-2} -4 z^2+2 a^4-3 a^2+ a^{-2} +1} |
| 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 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+4 z^{10} a^{-2} +9 z^{10}+8 a^3 z^9+2 a z^9-3 z^9 a^{-1} +3 z^9 a^{-3} +10 a^4 z^8-6 a^2 z^8-19 z^8 a^{-2} +z^8 a^{-4} -36 z^8+9 a^5 z^7-13 a^3 z^7-18 a z^7-11 z^7 a^{-1} -15 z^7 a^{-3} +6 a^6 z^6-19 a^4 z^6-10 a^2 z^6+30 z^6 a^{-2} -5 z^6 a^{-4} +50 z^6+3 a^7 z^5-14 a^5 z^5-a^3 z^5+14 a z^5+21 z^5 a^{-1} +23 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+15 a^4 z^4+15 a^2 z^4-21 z^4 a^{-2} +7 z^4 a^{-4} -35 z^4-2 a^7 z^3+11 a^5 z^3+9 a^3 z^3-3 a z^3-10 z^3 a^{-1} -11 z^3 a^{-3} -a^8 z^2+3 a^6 z^2-6 a^4 z^2-11 a^2 z^2+8 z^2 a^{-2} -2 z^2 a^{-4} +9 z^2-3 a^5 z-4 a^3 z-a z+z a^{-1} +z a^{-3} +2 a^4+3 a^2- a^{-2} +1} |
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