K12a374
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-15 q^3+23 q^2-27 q+30-28 q^{-1} +23 q^{-2} -16 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-40 t+49-40 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^2+1 }[/math] |
| Determinant | 189 |
| 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^4-7 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +12 z^4+2 a^4 z^2-9 a^2 z^2-8 z^2 a^{-2} +2 z^2 a^{-4} +14 z^2+a^4-4 a^2-2 a^{-2} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+4 z^{10} a^{-2} +8 z^{10}+7 a^3 z^9+15 a z^9+15 z^9 a^{-1} +7 z^9 a^{-3} +7 a^4 z^8+8 a^2 z^8+7 z^8 a^{-2} +7 z^8 a^{-4} +z^8+4 a^5 z^7-7 a^3 z^7-31 a z^7-34 z^7 a^{-1} -10 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-14 a^4 z^6-31 a^2 z^6-34 z^6 a^{-2} -17 z^6 a^{-4} +z^6 a^{-6} -32 z^6-9 a^5 z^5-7 a^3 z^5+20 a z^5+26 z^5 a^{-1} -2 z^5 a^{-3} -10 z^5 a^{-5} -2 a^6 z^4+8 a^4 z^4+29 a^2 z^4+41 z^4 a^{-2} +14 z^4 a^{-4} -2 z^4 a^{-6} +44 z^4+6 a^5 z^3+8 a^3 z^3-5 a z^3-5 z^3 a^{-1} +8 z^3 a^{-3} +6 z^3 a^{-5} +a^6 z^2-2 a^4 z^2-15 a^2 z^2-19 z^2 a^{-2} -5 z^2 a^{-4} -26 z^2-a^5 z-2 a^3 z-a z-z a^{-1} -z a^{-3} +a^4+4 a^2+2 a^{-2} +6 }[/math] |
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