K12a1042
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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^7+4 q^6-10 q^5+19 q^4-29 q^3+37 q^2-40 q+39-32 q^{-1} +23 q^{-2} -13 q^{-3} +5 q^{-4} - q^{-5} } |
| 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^4-11 t^3+30 t^2-52 t+63-52 t^{-1} +30 t^{-2} -11 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+5 z^6+4 z^4+z^2+1} |
| Determinant | 253 |
| 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^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +3 z^6-2 a^2 z^4+7 z^4 a^{-2} -3 z^4 a^{-4} +2 z^4-a^2 z^2+6 z^2 a^{-2} -3 z^2 a^{-4} -z^2+2 a^{-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 4 z^{11} a^{-1} +4 z^{11} a^{-3} +22 z^{10} a^{-2} +9 z^{10} a^{-4} +13 z^{10}+21 a z^9+23 z^9 a^{-1} +10 z^9 a^{-3} +8 z^9 a^{-5} +21 a^2 z^8-49 z^8 a^{-2} -22 z^8 a^{-4} +4 z^8 a^{-6} -2 z^8+13 a^3 z^7-28 a z^7-65 z^7 a^{-1} -49 z^7 a^{-3} -24 z^7 a^{-5} +z^7 a^{-7} +5 a^4 z^6-31 a^2 z^6+34 z^6 a^{-2} +18 z^6 a^{-4} -12 z^6 a^{-6} -32 z^6+a^5 z^5-13 a^3 z^5+4 a z^5+44 z^5 a^{-1} +54 z^5 a^{-3} +25 z^5 a^{-5} -3 z^5 a^{-7} -2 a^4 z^4+16 a^2 z^4-14 z^4 a^{-2} -8 z^4 a^{-4} +10 z^4 a^{-6} +22 z^4+4 a^3 z^3+5 a z^3-8 z^3 a^{-1} -23 z^3 a^{-3} -12 z^3 a^{-5} +2 z^3 a^{-7} -4 a^2 z^2+7 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} -2 z^2-a^3 z-2 a z+3 z a^{-3} +2 z a^{-5} -2 a^{-2} - a^{-4} } |
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