K12a51
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+17 q^2-24 q+29-29 q^{-1} +28 q^{-2} -21 q^{-3} +14 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+17 t^2-45 t+61-45 t^{-1} +17 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+5 z^4+5 z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+2 z^2 a^4-z^6 a^2+z^2 a^2+a^2-z^6+z^4+4 z^2+3+2 z^4 a^{-2} -2 a^{-2} -z^2 a^{-4} }[/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}+5 a^5 z^9+15 a^3 z^9+20 a z^9+10 z^9 a^{-1} +3 a^6 z^8-3 a^4 z^8-5 a^2 z^8+12 z^8 a^{-2} +13 z^8+a^7 z^7-15 a^5 z^7-53 a^3 z^7-51 a z^7-5 z^7 a^{-1} +9 z^7 a^{-3} -10 a^6 z^6-16 a^4 z^6-32 a^2 z^6-17 z^6 a^{-2} +4 z^6 a^{-4} -47 z^6-4 a^7 z^5+15 a^5 z^5+66 a^3 z^5+47 a z^5-14 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4+23 a^4 z^4+44 a^2 z^4+11 z^4 a^{-2} -4 z^4 a^{-4} +46 z^4+5 a^7 z^3-9 a^5 z^3-43 a^3 z^3-26 a z^3+13 z^3 a^{-1} +9 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2-9 a^4 z^2-18 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -20 z^2-2 a^7 z+4 a^5 z+13 a^3 z+8 a z-2 z a^{-1} -3 z a^{-3} +a^6-a^2+2 a^{-2} +3 }[/math] |
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