K12n186
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +10 q^{-2} -12 q^{-3} +15 q^{-4} -14 q^{-5} +12 q^{-6} -9 q^{-7} +5 q^{-8} -2 q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+11 t^2-18 t+21-18 t^{-1} +11 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+7 z^4+6 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^8-a^8-z^6 a^6-3 z^4 a^6-3 z^2 a^6-2 a^6+z^8 a^4+6 z^6 a^4+14 z^4 a^4+15 z^2 a^4+6 a^4-z^6 a^2-4 z^4 a^2-5 z^2 a^2-2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^3 a^{11}-2 z a^{11}+z^6 a^{10}+4 z^4 a^{10}-2 z^2 a^{10}+3 z^7 a^9+z a^9+4 z^8 a^8-3 z^6 a^8+2 z^2 a^8-a^8+3 z^9 a^7-6 z^5 a^7+z a^7+z^{10} a^6+7 z^8 a^6-22 z^6 a^6+17 z^4 a^6-9 z^2 a^6+2 a^6+6 z^9 a^5-11 z^7 a^5-6 z^5 a^5+12 z^3 a^5-5 z a^5+z^{10} a^4+6 z^8 a^4-30 z^6 a^4+36 z^4 a^4-20 z^2 a^4+6 a^4+3 z^9 a^3-7 z^7 a^3-4 z^5 a^3+14 z^3 a^3-5 z a^3+3 z^8 a^2-12 z^6 a^2+15 z^4 a^2-7 z^2 a^2+2 a^2+z^7 a-4 z^5 a+5 z^3 a-2 z a }[/math] |
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