K12n627
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+6 q^4-11 q^3+16 q^2-19 q+20-17 q^{-1} +14 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+12 t^2-25 t+33-25 t^{-1} +12 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+8 z^4+3 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-3 z^4 a^{-2} +15 z^4-7 a^2 z^2-5 z^2 a^{-2} -z^2 a^{-4} +16 z^2-3 a^2-3 a^{-2} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+5 a z^9+7 z^9 a^{-1} +2 z^9 a^{-3} +8 a^2 z^8+8 z^8 a^{-2} +z^8 a^{-4} +15 z^8+6 a^3 z^7+a z^7-2 z^7 a^{-1} +3 z^7 a^{-3} +3 a^4 z^6-15 a^2 z^6-18 z^6 a^{-2} +4 z^6 a^{-4} -40 z^6+a^5 z^5-9 a^3 z^5-17 a z^5-21 z^5 a^{-1} -11 z^5 a^{-3} +3 z^5 a^{-5} -4 a^4 z^4+18 a^2 z^4+13 z^4 a^{-2} -10 z^4 a^{-4} +45 z^4-2 a^5 z^3+6 a^3 z^3+21 a z^3+25 z^3 a^{-1} +7 z^3 a^{-3} -5 z^3 a^{-5} +a^4 z^2-14 a^2 z^2-8 z^2 a^{-2} +4 z^2 a^{-4} -27 z^2+a^5 z-2 a^3 z-8 a z-8 z a^{-1} -2 z a^{-3} +z a^{-5} +3 a^2+3 a^{-2} +7 }[/math] |
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