K12a774
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-5 q^3+8 q^2-11 q+13-13 q^{-1} +12 q^{-2} -9 q^{-3} +7 q^{-4} -4 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^2-22 t+33-22 t^{-1} +6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^4+2 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+z^4 a^4+z^2 a^4+a^4+2 z^4 a^2+2 z^2 a^2+a^2+2 z^4+z^2+z^4 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+5 a^2 z^{10}+3 z^{10}+2 a^5 z^9-a^3 z^9+a z^9+4 z^9 a^{-1} +2 a^6 z^8-7 a^4 z^8-24 a^2 z^8+4 z^8 a^{-2} -11 z^8+a^7 z^7-6 a^5 z^7-7 a^3 z^7-17 a z^7-13 z^7 a^{-1} +4 z^7 a^{-3} -9 a^6 z^6+7 a^4 z^6+46 a^2 z^6-9 z^6 a^{-2} +3 z^6 a^{-4} +18 z^6-5 a^7 z^5-a^5 z^5+15 a^3 z^5+40 a z^5+19 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-6 a^4 z^4-39 a^2 z^4+6 z^4 a^{-2} -7 z^4 a^{-4} -9 z^4+7 a^7 z^3+8 a^5 z^3-13 a^3 z^3-29 a z^3-9 z^3 a^{-1} +4 z^3 a^{-3} -2 z^3 a^{-5} -5 a^6 z^2+2 a^4 z^2+12 a^2 z^2+2 z^2 a^{-4} +3 z^2-3 a^7 z-3 a^5 z+3 a^3 z+5 a z+2 z a^{-1} +a^6+a^4-a^2 }[/math] |
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