K12a497
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+11 q^4-18 q^3+26 q^2-31 q+33-30 q^{-1} +24 q^{-2} -16 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+23 t^2-45 t+57-45 t^{-1} +23 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^4+1 }[/math] |
| Determinant | 209 |
| 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^4-7 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +12 z^4+2 a^4 z^2-9 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} +12 z^2+a^4-3 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+5 z^{10} a^{-2} +9 z^{10}+7 a^3 z^9+18 a z^9+21 z^9 a^{-1} +10 z^9 a^{-3} +7 a^4 z^8+11 a^2 z^8+13 z^8 a^{-2} +10 z^8 a^{-4} +7 z^8+4 a^5 z^7-6 a^3 z^7-36 a z^7-44 z^7 a^{-1} -13 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-14 a^4 z^6-39 a^2 z^6-51 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -53 z^6-9 a^5 z^5-8 a^3 z^5+20 a z^5+23 z^5 a^{-1} -5 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+9 a^4 z^4+39 a^2 z^4+46 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +61 z^4+6 a^5 z^3+9 a^3 z^3+2 z^3 a^{-1} +8 z^3 a^{-3} +3 z^3 a^{-5} +a^6 z^2-3 a^4 z^2-18 a^2 z^2-14 z^2 a^{-2} -2 z^2 a^{-4} -26 z^2-a^5 z-2 a^3 z-2 a z-2 z a^{-1} -z a^{-3} +a^4+3 a^2+ a^{-2} +4 }[/math] |
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