K12a453
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-12 q^3+18 q^2-22 q+23-22 q^{-1} +18 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+18 t^2-30 t+37-30 t^{-1} +18 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-4 z^4-5 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-8 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} +10 z^4+3 a^4 z^2-10 a^2 z^2-10 z^2 a^{-2} +3 z^2 a^{-4} +9 z^2+2 a^4-3 a^2-3 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+5 a^3 z^9+7 a z^9+7 z^9 a^{-1} +5 z^9 a^{-3} +5 a^4 z^8+2 a^2 z^8+z^8 a^{-2} +5 z^8 a^{-4} -7 z^8+3 a^5 z^7-9 a^3 z^7-17 a z^7-18 z^7 a^{-1} -10 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-13 a^4 z^6-19 a^2 z^6-13 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} -4 z^6-8 a^5 z^5+3 a^3 z^5+13 a z^5+19 z^5 a^{-1} +9 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+12 a^4 z^4+28 a^2 z^4+19 z^4 a^{-2} +12 z^4 a^{-4} -3 z^4 a^{-6} +17 z^4+5 a^5 z^3+a^3 z^3+a z^3-8 z^3 a^{-1} -8 z^3 a^{-3} +5 z^3 a^{-5} +2 a^6 z^2-8 a^4 z^2-16 a^2 z^2-14 z^2 a^{-2} -7 z^2 a^{-4} +2 z^2 a^{-6} -11 z^2-a^5 z-a^3 z-2 a z+2 z a^{-3} +2 a^4+3 a^2+3 a^{-2} +2 a^{-4} +3 }[/math] |
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