K12a291
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+8 q^6-13 q^5+19 q^4-22 q^3+23 q^2-22 q+18-12 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+17 t^2-34 t+43-34 t^{-1} +17 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-7 z^4-2 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-6 z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-6} -2 z^4+2 a^2 z^2-7 z^2 a^{-2} +3 z^2 a^{-4} +z^2 a^{-6} -z^2+a^2-4 a^{-2} +4 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +11 z^{10} a^{-4} +5 z^{10} a^{-6} +10 z^9 a^{-1} +10 z^9 a^{-3} +4 z^9 a^{-5} +4 z^9 a^{-7} -2 z^8 a^{-2} -33 z^8 a^{-4} -19 z^8 a^{-6} +z^8 a^{-8} +11 z^8+9 a z^7-17 z^7 a^{-1} -46 z^7 a^{-3} -38 z^7 a^{-5} -18 z^7 a^{-7} +6 a^2 z^6-32 z^6 a^{-2} +15 z^6 a^{-4} +18 z^6 a^{-6} -4 z^6 a^{-8} -19 z^6+3 a^3 z^5-12 a z^5+z^5 a^{-1} +41 z^5 a^{-3} +50 z^5 a^{-5} +25 z^5 a^{-7} +a^4 z^4-6 a^2 z^4+40 z^4 a^{-2} +18 z^4 a^{-4} +z^4 a^{-6} +5 z^4 a^{-8} +11 z^4-2 a^3 z^3+8 a z^3+6 z^3 a^{-1} -10 z^3 a^{-3} -16 z^3 a^{-5} -10 z^3 a^{-7} -a^4 z^2+4 a^2 z^2-21 z^2 a^{-2} -17 z^2 a^{-4} -5 z^2 a^{-6} -2 z^2 a^{-8} -2 z^2-2 a z-2 z a^{-1} -a^2+4 a^{-2} +4 a^{-4} + a^{-6} +1 }[/math] |
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