K12n189
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+7 q^5-10 q^4+13 q^3-13 q^2+12 q-9+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-9 t^2+16 t-19+16 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-5 z^4+1 }[/math] |
| Determinant | 79 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4-11 z^2 a^{-2} +6 z^2 a^{-4} +5 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +3 z^9 a^{-1} +5 z^9 a^{-3} +2 z^9 a^{-5} +4 z^8 a^{-2} +z^8 a^{-4} +z^8 a^{-6} +4 z^8+3 a z^7-5 z^7 a^{-1} -13 z^7 a^{-3} -5 z^7 a^{-5} +a^2 z^6-18 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} -11 z^6-9 a z^5-2 z^5 a^{-1} +15 z^5 a^{-3} +12 z^5 a^{-5} +4 z^5 a^{-7} -3 a^2 z^4+24 z^4 a^{-2} +12 z^4 a^{-4} +z^4 a^{-8} +8 z^4+6 a z^3+3 z^3 a^{-1} -6 z^3 a^{-3} -8 z^3 a^{-5} -5 z^3 a^{-7} +2 a^2 z^2-15 z^2 a^{-2} -9 z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} -5 z^2-a z-z a^{-1} +z a^{-3} +z a^{-5} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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