K12a783
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+23 q^5-28 q^4+30 q^3-27 q^2+22 q-15+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-16 t^2+45 t-61+45 t^{-1} -16 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-4 z^4-z^2+1 }[/math] |
| Determinant | 187 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10} a^{-6} +6 z^9 a^{-1} +9 z^9 a^{-3} +13 z^9 a^{-5} +10 z^9 a^{-7} -4 z^8 a^{-2} -27 z^8 a^{-4} -10 z^8 a^{-6} +8 z^8 a^{-8} +5 z^8+3 a z^7-8 z^7 a^{-1} -29 z^7 a^{-3} -48 z^7 a^{-5} -26 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6+z^6 a^{-2} +28 z^6 a^{-4} -3 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -8 z^6-7 a z^5+2 z^5 a^{-1} +39 z^5 a^{-3} +64 z^5 a^{-5} +25 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4-6 z^4 a^{-2} -12 z^4 a^{-4} +13 z^4 a^{-6} +14 z^4 a^{-8} -2 z^4 a^{-10} +5 a z^3-3 z^3 a^{-1} -27 z^3 a^{-3} -33 z^3 a^{-5} -11 z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2+3 z^2 a^{-2} +2 z^2 a^{-4} -4 z^2 a^{-6} -4 z^2 a^{-8} +4 z^2-a z+z a^{-1} +6 z a^{-3} +6 z a^{-5} +2 z a^{-7} -a^2- a^{-2} -1 }[/math] |
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