K12a942
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+7 q^6-13 q^5+19 q^4-24 q^3+27 q^2-26 q+22-16 q^{-1} +10 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-39 t+51-39 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4-3 z^2+1 }[/math] |
| Determinant | 173 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-5 z^4 a^{-2} -2 z^4 a^{-4} +z^4 a^{-6} -z^4+a^2 z^2-4 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +a^2- a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +11 z^{10} a^{-4} +4 z^{10} a^{-6} +14 z^9 a^{-1} +13 z^9 a^{-3} +2 z^9 a^{-5} +3 z^9 a^{-7} +3 z^8 a^{-2} -31 z^8 a^{-4} -15 z^8 a^{-6} +z^8 a^{-8} +18 z^8+16 a z^7-19 z^7 a^{-1} -48 z^7 a^{-3} -27 z^7 a^{-5} -14 z^7 a^{-7} +10 a^2 z^6-43 z^6 a^{-2} +17 z^6 a^{-4} +16 z^6 a^{-6} -5 z^6 a^{-8} -29 z^6+4 a^3 z^5-21 a z^5-5 z^5 a^{-1} +35 z^5 a^{-3} +37 z^5 a^{-5} +22 z^5 a^{-7} +a^4 z^4-8 a^2 z^4+37 z^4 a^{-2} +4 z^4 a^{-4} -4 z^4 a^{-6} +8 z^4 a^{-8} +12 z^4+9 a z^3+5 z^3 a^{-1} -5 z^3 a^{-3} -14 z^3 a^{-5} -13 z^3 a^{-7} +4 a^2 z^2-10 z^2 a^{-2} +z^2 a^{-4} +z^2 a^{-6} -4 z^2 a^{-8} -2 z^2-a z-z a^{-1} +2 z a^{-5} +2 z a^{-7} -a^2- a^{-4} - a^{-6} }[/math] |
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