K12a756
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+16 q-23+28 q^{-1} -29 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+39 t-45+39 t^{-1} -23 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+5 z^4+3 z^2+1 }[/math] |
| Determinant | 187 |
| 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} +4 z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+12 a^2 z^{10}+6 z^{10}+9 a^5 z^9+13 a^3 z^9+11 a z^9+7 z^9 a^{-1} +9 a^6 z^8+a^4 z^8-23 a^2 z^8+4 z^8 a^{-2} -11 z^8+6 a^7 z^7-11 a^5 z^7-38 a^3 z^7-44 a z^7-22 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-15 a^6 z^6-22 a^4 z^6+5 a^2 z^6-13 z^6 a^{-2} -4 z^6+a^9 z^5-8 a^7 z^5+2 a^5 z^5+31 a^3 z^5+44 a z^5+21 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+16 a^6 z^4+28 a^4 z^4+6 a^2 z^4+12 z^4 a^{-2} +10 z^4-2 a^9 z^3+5 a^7 z^3+8 a^5 z^3-8 a^3 z^3-19 a z^3-8 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-9 a^6 z^2-13 a^4 z^2-3 a^2 z^2-3 z^2 a^{-2} -3 z^2+a^9 z-2 a^7 z-4 a^5 z+2 a z+z a^{-1} +2 a^6+3 a^4 }[/math] |
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