K12a81
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+13 q^5-18 q^4+23 q^3-25 q^2+23 q-19+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+38 t-51+38 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4+1 }[/math] |
| Determinant | 159 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-a^2 z^4-3 z^4 a^{-4} +2 z^4-a^2 z^2-2 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2-2 a^{-2} +2 a^{-6} - a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +3 z^{10} a^{-4} +4 z^{10}+6 a z^9+11 z^9 a^{-1} +10 z^9 a^{-3} +5 z^9 a^{-5} +4 a^2 z^8-6 z^8 a^{-2} +7 z^8 a^{-4} +6 z^8 a^{-6} -3 z^8+a^3 z^7-19 a z^7-38 z^7 a^{-1} -22 z^7 a^{-3} +z^7 a^{-5} +5 z^7 a^{-7} -14 a^2 z^6-20 z^6 a^{-2} -21 z^6 a^{-4} -5 z^6 a^{-6} +3 z^6 a^{-8} -21 z^6-3 a^3 z^5+16 a z^5+36 z^5 a^{-1} +13 z^5 a^{-3} -11 z^5 a^{-5} -6 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+30 z^4 a^{-2} +17 z^4 a^{-4} -z^4 a^{-6} -5 z^4 a^{-8} +31 z^4+2 a^3 z^3-4 a z^3-16 z^3 a^{-1} -5 z^3 a^{-3} +9 z^3 a^{-5} +2 z^3 a^{-7} -2 z^3 a^{-9} -4 a^2 z^2-16 z^2 a^{-2} -5 z^2 a^{-4} +4 z^2 a^{-6} +3 z^2 a^{-8} -14 z^2+a z+4 z a^{-1} +3 z a^{-3} -z a^{-5} +z a^{-9} +2 a^{-2} -2 a^{-6} - a^{-8} +2 }[/math] |
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