K12a584
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-8 q^6+13 q^5-18 q^4+21 q^3-22 q^2+20 q-15+11 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-19 t^2+29 t-31+29 t^{-1} -19 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+3 z^4+1 }[/math] |
| Determinant | 143 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-10 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +8 z^4-3 a^2 z^2-10 z^2 a^{-2} +6 z^2 a^{-4} -2 z^2 a^{-6} +9 z^2-a^2-3 a^{-2} + a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10}+4 a z^9+7 z^9 a^{-1} +10 z^9 a^{-3} +7 z^9 a^{-5} +3 a^2 z^8-16 z^8 a^{-2} -z^8 a^{-4} +8 z^8 a^{-6} -4 z^8+a^3 z^7-13 a z^7-32 z^7 a^{-1} -36 z^7 a^{-3} -11 z^7 a^{-5} +7 z^7 a^{-7} -12 a^2 z^6+5 z^6 a^{-2} -10 z^6 a^{-4} -12 z^6 a^{-6} +4 z^6 a^{-8} -13 z^6-4 a^3 z^5+9 a z^5+39 z^5 a^{-1} +46 z^5 a^{-3} +8 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+14 z^4 a^{-2} +14 z^4 a^{-4} +4 z^4 a^{-6} -6 z^4 a^{-8} +24 z^4+4 a^3 z^3-17 z^3 a^{-1} -20 z^3 a^{-3} -3 z^3 a^{-5} +3 z^3 a^{-7} -z^3 a^{-9} -7 a^2 z^2-12 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-8} -15 z^2-a^3 z-a z+z a^{-1} +z a^{-3} +a^2+3 a^{-2} + a^{-4} +4 }[/math] |
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