K12a1227
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+16 q-22+28 q^{-1} -30 q^{-2} +28 q^{-3} -23 q^{-4} +16 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+13 t^3-24 t^2+34 t-37+34 t^{-1} -24 t^{-2} +13 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+5 z^8+8 z^6+4 z^4+1 }[/math] |
| Determinant | 191 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+7 a^2 z^8-z^8-5 a^4 z^6+18 a^2 z^6-5 z^6-8 a^4 z^4+20 a^2 z^4-8 z^4-4 a^4 z^2+8 a^2 z^2-4 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+15 a^2 z^{10}+7 z^{10}+11 a^5 z^9+8 a^3 z^9+4 a z^9+7 z^9 a^{-1} +11 a^6 z^8-10 a^4 z^8-44 a^2 z^8+4 z^8 a^{-2} -19 z^8+8 a^7 z^7-17 a^5 z^7-32 a^3 z^7-30 a z^7-22 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-17 a^6 z^6+2 a^4 z^6+51 a^2 z^6-13 z^6 a^{-2} +15 z^6+a^9 z^5-11 a^7 z^5+8 a^5 z^5+32 a^3 z^5+34 a z^5+19 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+9 a^6 z^4+2 a^4 z^4-31 a^2 z^4+11 z^4 a^{-2} -8 z^4-a^9 z^3+4 a^7 z^3+3 a^5 z^3-10 a^3 z^3-16 a z^3-6 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-a^6 z^2+a^4 z^2+7 a^2 z^2-2 z^2 a^{-2} +2 z^2-a^7 z-2 a^5 z+2 a z+z a^{-1} +1 }[/math] |
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