K12a468
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-10 q^2+17 q-23+29 q^{-1} -30 q^{-2} +28 q^{-3} -22 q^{-4} +15 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-23 t^2+40 t-47+40 t^{-1} -23 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+5 z^4+4 z^2+1 }[/math] |
| Determinant | 191 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-6 a^2 z^4-z^4 a^{-2} +6 z^4-3 a^6 z^2+8 a^4 z^2-4 a^2 z^2-2 z^2 a^{-2} +5 z^2-2 a^6+3 a^4-a^2- a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+7 a^4 z^{10}+13 a^2 z^{10}+6 z^{10}+10 a^5 z^9+17 a^3 z^9+14 a z^9+7 z^9 a^{-1} +9 a^6 z^8-4 a^4 z^8-24 a^2 z^8+4 z^8 a^{-2} -7 z^8+6 a^7 z^7-18 a^5 z^7-61 a^3 z^7-57 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-15 a^6 z^6-17 a^4 z^6-7 a^2 z^6-12 z^6 a^{-2} -20 z^6+a^9 z^5-8 a^7 z^5+18 a^5 z^5+74 a^3 z^5+62 a z^5+12 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+15 a^6 z^4+32 a^4 z^4+31 a^2 z^4+11 z^4 a^{-2} +29 z^4-2 a^9 z^3+4 a^7 z^3-8 a^5 z^3-39 a^3 z^3-31 a z^3-3 z^3 a^{-1} +3 z^3 a^{-3} +a^8 z^2-9 a^6 z^2-18 a^4 z^2-15 a^2 z^2-5 z^2 a^{-2} -12 z^2+a^9 z-a^7 z+a^5 z+8 a^3 z+7 a z+z a^{-1} -z a^{-3} +2 a^6+3 a^4+a^2+ a^{-2} +2 }[/math] |
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