K12a1148
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+4 q^6-6 q^5+8 q^4-10 q^3+10 q^2-10 q+9-6 q^{-1} +4 q^{-2} -2 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+9 t^2-15 t+19-15 t^{-1} +9 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-9 z^4-6 z^2+1 }[/math] |
| Determinant | 73 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-3 z^4 a^{-2} -4 z^4 a^{-4} +z^4 a^{-6} -4 z^4+3 a^2 z^2-2 z^2 a^{-2} -5 z^2 a^{-4} +3 z^2 a^{-6} -5 z^2+2 a^2-2 a^{-4} +2 a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +3 z^9 a^{-1} -2 z^9 a^{-3} -3 z^9 a^{-5} +2 z^9 a^{-7} -6 z^8 a^{-2} -20 z^8 a^{-4} -10 z^8 a^{-6} +z^8 a^{-8} +3 z^8+3 a z^7-10 z^7 a^{-1} -z^7 a^{-3} +z^7 a^{-5} -11 z^7 a^{-7} +3 a^2 z^6+7 z^6 a^{-2} +38 z^6 a^{-4} +16 z^6 a^{-6} -6 z^6 a^{-8} -6 z^6+2 a^3 z^5-5 a z^5+17 z^5 a^{-1} +3 z^5 a^{-3} -3 z^5 a^{-5} +18 z^5 a^{-7} +a^4 z^4-6 a^2 z^4-4 z^4 a^{-2} -40 z^4 a^{-4} -14 z^4 a^{-6} +11 z^4 a^{-8} +4 z^4-3 a^3 z^3+4 a z^3-14 z^3 a^{-1} -5 z^3 a^{-3} +7 z^3 a^{-5} -9 z^3 a^{-7} -2 a^4 z^2+6 a^2 z^2-2 z^2 a^{-2} +18 z^2 a^{-4} +10 z^2 a^{-6} -6 z^2 a^{-8} +4 z^2+a z+4 z a^{-1} -2 z a^{-5} +z a^{-7} -2 a^2-2 a^{-4} -2 a^{-6} -1 }[/math] |
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