K12a183
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-11 q^3+15 q^2-18 q+19-17 q^{-1} +13 q^{-2} -9 q^{-3} +5 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^2-30 t+49-30 t^{-1} +6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^4-6 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-2 z^2 a^4+z^4 a^2-3 z^2 a^2-2 a^2+3 z^4+2 z^2+2+2 z^4 a^{-2} -3 z^2 a^{-4} - a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+4 a^3 z^9+5 a z^9+5 z^9 a^{-1} +4 z^9 a^{-3} +3 a^4 z^8-7 a^2 z^8-4 z^8 a^{-2} +4 z^8 a^{-4} -18 z^8+2 a^5 z^7-14 a^3 z^7-30 a z^7-23 z^7 a^{-1} -6 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-8 a^4 z^6+2 a^2 z^6-7 z^6 a^{-4} +z^6 a^{-6} +19 z^6-6 a^5 z^5+22 a^3 z^5+59 a z^5+37 z^5 a^{-1} -2 z^5 a^{-3} -8 z^5 a^{-5} -4 a^6 z^4+4 a^4 z^4+13 a^2 z^4-3 z^4 a^{-4} -3 z^4 a^{-6} +5 z^4+3 a^5 z^3-20 a^3 z^3-40 a z^3-22 z^3 a^{-1} +5 z^3 a^{-5} +4 a^6 z^2-a^4 z^2-12 a^2 z^2+4 z^2 a^{-4} +3 z^2 a^{-6} -8 z^2+6 a^3 z+9 a z+5 z a^{-1} +z a^{-3} -z a^{-5} -a^6+2 a^2- a^{-4} - a^{-6} +2 }[/math] |
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