K12a963
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+10 q^2-18 q+26-32 q^{-1} +35 q^{-2} -32 q^{-3} +27 q^{-4} -19 q^{-5} +11 q^{-6} -5 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+24 t^2-50 t+63-50 t^{-1} +24 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-6 z^4+z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^6-2 a^6-z^6 a^4+z^4 a^4+7 z^2 a^4+5 a^4-3 z^6 a^2-9 z^4 a^2-10 z^2 a^2-4 a^2-z^6+3 z^2+2+z^4 a^{-2} +z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^5 z^{11}+4 a^3 z^{11}+8 a^6 z^{10}+22 a^4 z^{10}+14 a^2 z^{10}+5 a^7 z^9+5 a^5 z^9+23 a^3 z^9+23 a z^9+a^8 z^8-28 a^6 z^8-66 a^4 z^8-13 a^2 z^8+24 z^8-19 a^7 z^7-59 a^5 z^7-104 a^3 z^7-46 a z^7+18 z^7 a^{-1} -3 a^8 z^6+26 a^6 z^6+39 a^4 z^6-44 a^2 z^6+10 z^6 a^{-2} -44 z^6+23 a^7 z^5+81 a^5 z^5+106 a^3 z^5+21 a z^5-23 z^5 a^{-1} +4 z^5 a^{-3} +3 a^8 z^4+20 a^4 z^4+56 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +26 z^4-8 a^7 z^3-29 a^5 z^3-36 a^3 z^3-5 a z^3+10 z^3 a^{-1} -a^8 z^2-6 a^6 z^2-19 a^4 z^2-25 a^2 z^2+2 z^2 a^{-2} -9 z^2-a^7 z+a^5 z+3 a^3 z-z a^{-1} +2 a^6+5 a^4+4 a^2+2 }[/math] |
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