K12a282
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-20 q^3+29 q^2-35 q+37-34 q^{-1} +27 q^{-2} -18 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+26 t^2-50 t+63-50 t^{-1} +26 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^4-2 z^2+1 }[/math] |
| Determinant | 233 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +7 z^4+2 a^4 z^2-6 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} +4 z^2+a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+8 z^{10} a^{-2} +14 z^{10}+9 a^3 z^9+19 a z^9+23 z^9 a^{-1} +13 z^9 a^{-3} +8 a^4 z^8+7 a^2 z^8+3 z^8 a^{-2} +11 z^8 a^{-4} -9 z^8+4 a^5 z^7-11 a^3 z^7-42 a z^7-55 z^7 a^{-1} -23 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-34 a^2 z^6-33 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -27 z^6-8 a^5 z^5-a^3 z^5+26 a z^5+37 z^5 a^{-1} +10 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+12 a^4 z^4+32 a^2 z^4+27 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +32 z^4+5 a^5 z^3+4 a^3 z^3-3 a z^3-5 z^3 a^{-1} -z^3 a^{-3} +2 z^3 a^{-5} +a^6 z^2-5 a^4 z^2-12 a^2 z^2-4 z^2 a^{-2} -2 z^2 a^{-4} -8 z^2-a^5 z-a^3 z-a z-z a^{-1} +a^4+a^2- a^{-2} }[/math] |
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