K12a208
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-14 q^3+21 q^2-24 q+26-24 q^{-1} +19 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-39 t+55-39 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4-z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-2 a^4+3 z^4 a^2+3 z^2 a^2+a^2-z^6+z^2+1-z^6 a^{-2} -2 z^4 a^{-2} -3 z^2 a^{-2} +z^4 a^{-4} +z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+4 z^{10} a^{-2} +7 z^{10}+4 a^3 z^9+9 a z^9+12 z^9 a^{-1} +7 z^9 a^{-3} +4 a^4 z^8+2 a^2 z^8+3 z^8 a^{-2} +7 z^8 a^{-4} -6 z^8+3 a^5 z^7-a^3 z^7-21 a z^7-34 z^7 a^{-1} -13 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-5 a^4 z^6-7 a^2 z^6-28 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} -10 z^6-8 a^5 z^5-10 a^3 z^5+23 a z^5+38 z^5 a^{-1} +3 z^5 a^{-3} -10 z^5 a^{-5} -3 a^6 z^4-5 a^4 z^4-a^2 z^4+38 z^4 a^{-2} +14 z^4 a^{-4} -2 z^4 a^{-6} +23 z^4+7 a^5 z^3+7 a^3 z^3-16 a z^3-18 z^3 a^{-1} +3 z^3 a^{-3} +5 z^3 a^{-5} +3 a^6 z^2+8 a^4 z^2+3 a^2 z^2-16 z^2 a^{-2} -5 z^2 a^{-4} -13 z^2-2 a^5 z-a^3 z+4 a z+4 z a^{-1} +z a^{-3} -a^6-2 a^4-a^2+1 }[/math] |
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