K12a20
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+16 q^2-23 q+29-30 q^{-1} +28 q^{-2} -23 q^{-3} +16 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-41 t+51-41 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +5 z^6+3 a^4 z^4-11 a^2 z^4-3 z^4 a^{-2} +11 z^4-a^6 z^2+7 a^4 z^2-14 a^2 z^2-3 z^2 a^{-2} +11 z^2-a^6+4 a^4-6 a^2- a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+9 a^2 z^{10}+5 z^{10}+6 a^5 z^9+17 a^3 z^9+21 a z^9+10 z^9 a^{-1} +4 a^6 z^8+4 a^4 z^8+2 a^2 z^8+11 z^8 a^{-2} +13 z^8+a^7 z^7-15 a^5 z^7-51 a^3 z^7-53 a z^7-10 z^7 a^{-1} +8 z^7 a^{-3} -13 a^6 z^6-41 a^4 z^6-60 a^2 z^6-17 z^6 a^{-2} +4 z^6 a^{-4} -53 z^6-3 a^7 z^5+7 a^5 z^5+39 a^3 z^5+39 a z^5-2 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +14 a^6 z^4+51 a^4 z^4+79 a^2 z^4+13 z^4 a^{-2} -5 z^4 a^{-4} +60 z^4+3 a^7 z^3+3 a^5 z^3-8 a^3 z^3-7 a z^3+7 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -6 a^6 z^2-24 a^4 z^2-38 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -27 z^2-a^7 z-2 a^5 z-a^3 z-a z-2 z a^{-1} -z a^{-3} +a^6+4 a^4+6 a^2+ a^{-2} +5 }[/math] |
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