K12a1031
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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^3+2 q^2-4 q+8-10 q^{-1} +13 q^{-2} -14 q^{-3} +14 q^{-4} -12 q^{-5} +9 q^{-6} -6 q^{-7} +3 q^{-8} - q^{-9} } |
| 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^4-7 t^3+13 t^2-17 t+19-17 t^{-1} +13 t^{-2} -7 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+9 z^6+11 z^4+4 z^2+1} |
| Determinant | 97 |
| Signature | -4 |
| 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^4 z^8+a^2 z^8-a^6 z^6+5 a^4 z^6+6 a^2 z^6-z^6-4 a^6 z^4+7 a^4 z^4+13 a^2 z^4-5 z^4-4 a^6 z^2+2 a^4 z^2+13 a^2 z^2-7 z^2-a^6-a^4+5 a^2-2} |
| 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 z^3 a^{11}+3 z^4 a^{10}+6 z^5 a^9-4 z^3 a^9+z a^9+9 z^6 a^8-12 z^4 a^8+3 z^2 a^8+11 z^7 a^7-22 z^5 a^7+9 z^3 a^7-2 z a^7+11 z^8 a^6-29 z^6 a^6+19 z^4 a^6-8 z^2 a^6+a^6+8 z^9 a^5-21 z^7 a^5+5 z^5 a^5+7 z^3 a^5-2 z a^5+4 z^{10} a^4-6 z^8 a^4-20 z^6 a^4+31 z^4 a^4-7 z^2 a^4-a^4+z^{11} a^3+6 z^9 a^3-42 z^7 a^3+63 z^5 a^3-30 z^3 a^3+6 z a^3+6 z^{10} a^2-30 z^8 a^2+48 z^6 a^2-33 z^4 a^2+17 z^2 a^2-5 a^2+z^{11} a-z^9 a-17 z^7 a+47 z^5 a-39 z^3 a+9 z a+2 z^{10}-13 z^8+30 z^6-30 z^4+13 z^2-2+z^9 a^{-1} -7 z^7 a^{-1} +17 z^5 a^{-1} -16 z^3 a^{-1} +4 z a^{-1} } |
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