K12a583
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-14 q^3+20 q^2-24 q+25-23 q^{-1} +18 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+19 t^2-33 t+41-33 t^{-1} +19 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-3 z^4-4 z^2+1 }[/math] |
| Determinant | 161 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-8 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +10 z^4+3 a^4 z^2-10 a^2 z^2-7 z^2 a^{-2} +2 z^2 a^{-4} +8 z^2+2 a^4-3 a^2- a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+4 z^{10} a^{-2} +7 z^{10}+5 a^3 z^9+9 a z^9+11 z^9 a^{-1} +7 z^9 a^{-3} +5 a^4 z^8+3 a^2 z^8+z^8 a^{-2} +7 z^8 a^{-4} -8 z^8+3 a^5 z^7-9 a^3 z^7-25 a z^7-30 z^7 a^{-1} -13 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-13 a^4 z^6-22 a^2 z^6-16 z^6 a^{-2} -16 z^6 a^{-4} +z^6 a^{-6} -7 z^6-8 a^5 z^5+4 a^3 z^5+26 a z^5+29 z^5 a^{-1} +6 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4+12 a^4 z^4+32 a^2 z^4+15 z^4 a^{-2} +9 z^4 a^{-4} -2 z^4 a^{-6} +21 z^4+5 a^5 z^3-a^3 z^3-7 a z^3-9 z^3 a^{-1} -4 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2-8 a^4 z^2-18 a^2 z^2-6 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} -10 z^2-a^5 z+z a^{-3} +2 a^4+3 a^2+ a^{-2} + a^{-4} +2 }[/math] |
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