K12n859
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-16 q^3+22 q^2-25 q+24-21 q^{-1} +15 q^{-2} -8 q^{-3} +3 q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+16 t^2-31 t+41-31 t^{-1} +16 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6-5 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-2 z^6 a^{-2} +5 z^6-4 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +10 z^4+a^4 z^2-7 a^2 z^2-9 z^2 a^{-2} +2 z^2 a^{-4} +8 z^2+2 a^4-3 a^2-3 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-2} +3 z^{10}+8 a z^9+16 z^9 a^{-1} +8 z^9 a^{-3} +8 a^2 z^8+12 z^8 a^{-2} +8 z^8 a^{-4} +12 z^8+3 a^3 z^7-10 a z^7-30 z^7 a^{-1} -13 z^7 a^{-3} +4 z^7 a^{-5} -13 a^2 z^6-40 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} -34 z^6+3 a^3 z^5+6 a z^5+15 z^5 a^{-1} +4 z^5 a^{-3} -8 z^5 a^{-5} +6 a^4 z^4+18 a^2 z^4+33 z^4 a^{-2} +14 z^4 a^{-4} -2 z^4 a^{-6} +29 z^4-5 a^3 z^3+a z^3-z^3 a^{-1} -3 z^3 a^{-3} +4 z^3 a^{-5} -8 a^4 z^2-13 a^2 z^2-14 z^2 a^{-2} -7 z^2 a^{-4} +z^2 a^{-6} -11 z^2+a^3 z-2 a z-2 z a^{-1} +z a^{-3} +2 a^4+3 a^2+3 a^{-2} +2 a^{-4} +3 }[/math] |
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