K12a965
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-24 q^3+36 q^2-44 q+48-45 q^{-1} +36 q^{-2} -25 q^{-3} +14 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+32 t^2-65 t+83-65 t^{-1} +32 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 297 |
| 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^2-3 a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} +z^2+a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a z^{11}+5 z^{11} a^{-1} +15 a^2 z^{10}+14 z^{10} a^{-2} +29 z^{10}+19 a^3 z^9+29 a z^9+27 z^9 a^{-1} +17 z^9 a^{-3} +13 a^4 z^8-13 a^2 z^8-11 z^8 a^{-2} +12 z^8 a^{-4} -49 z^8+5 a^5 z^7-37 a^3 z^7-87 a z^7-80 z^7 a^{-1} -30 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-23 a^4 z^6-18 a^2 z^6-17 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} +11 z^6-6 a^5 z^5+27 a^3 z^5+77 a z^5+69 z^5 a^{-1} +18 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+14 a^4 z^4+24 a^2 z^4+20 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +16 z^4+a^5 z^3-12 a^3 z^3-28 a z^3-23 z^3 a^{-1} -6 z^3 a^{-3} +2 z^3 a^{-5} -6 a^4 z^2-10 a^2 z^2-5 z^2 a^{-2} -3 z^2 a^{-4} -6 z^2+3 a^3 z+5 a z+3 z a^{-1} +z a^{-3} +a^4+a^2- a^{-2} }[/math] |
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