K12a1228
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+17 q^2-24 q+29-31 q^{-1} +29 q^{-2} -23 q^{-3} +16 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+24 t^2-39 t+47-39 t^{-1} +24 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+4 z^4-z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-z^6 a^{-2} +4 z^6-3 a^4 z^4+5 a^2 z^4-3 z^4 a^{-2} +5 z^4-2 a^4 z^2+2 a^2 z^2-2 z^2 a^{-2} +z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+7 a^4 z^{10}+16 a^2 z^{10}+9 z^{10}+7 a^5 z^9+6 a^3 z^9+12 a z^9+13 z^9 a^{-1} +4 a^6 z^8-18 a^4 z^8-46 a^2 z^8+12 z^8 a^{-2} -12 z^8+a^7 z^7-22 a^5 z^7-39 a^3 z^7-50 a z^7-26 z^7 a^{-1} +8 z^7 a^{-3} -13 a^6 z^6+12 a^4 z^6+49 a^2 z^6-20 z^6 a^{-2} +4 z^6 a^{-4} -3 a^7 z^5+20 a^5 z^5+50 a^3 z^5+62 a z^5+24 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-5 a^4 z^4-25 a^2 z^4+12 z^4 a^{-2} -5 z^4 a^{-4} +8 z^4+2 a^7 z^3-8 a^5 z^3-29 a^3 z^3-31 a z^3-9 z^3 a^{-1} +2 z^3 a^{-3} -z^3 a^{-5} -2 a^6 z^2+a^4 z^2+5 a^2 z^2-z^2 a^{-2} +z^2 a^{-4} +2 a^5 z+6 a^3 z+5 a z+z a^{-1} -a^2- a^{-2} -1 }[/math] |
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