K12a458
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-24 q^3+35 q^2-43 q+47-43 q^{-1} +35 q^{-2} -24 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+32 t^2-63 t+79-63 t^{-1} +32 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-2 z^4+1 }[/math] |
| Determinant | 289 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +4 z^4+a^4 z^2-2 a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +11 a^2 z^{10}+11 z^{10} a^{-2} +22 z^{10}+16 a^3 z^9+35 a z^9+35 z^9 a^{-1} +16 z^9 a^{-3} +12 a^4 z^8+6 a^2 z^8+6 z^8 a^{-2} +12 z^8 a^{-4} -12 z^8+5 a^5 z^7-25 a^3 z^7-84 a z^7-84 z^7 a^{-1} -25 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-47 a^2 z^6-47 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -50 z^6-7 a^5 z^5+12 a^3 z^5+60 a z^5+60 z^5 a^{-1} +12 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+14 a^4 z^4+40 a^2 z^4+40 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +50 z^4+3 a^5 z^3-3 a^3 z^3-19 a z^3-19 z^3 a^{-1} -3 z^3 a^{-3} +3 z^3 a^{-5} -4 a^4 z^2-10 a^2 z^2-10 z^2 a^{-2} -4 z^2 a^{-4} -12 z^2+a^3 z+3 a z+3 z a^{-1} +z a^{-3} +1 }[/math] |
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