K12a651
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+6 q^8-9 q^7+12 q^6-14 q^5+14 q^4-13 q^3+10 q^2-7 q+5-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+15 t^2-17 t+17-17 t^{-1} +15 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-7 z^4-4 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -9 z^4 a^{-2} +8 z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-8} +z^4-10 z^2 a^{-2} +6 z^2 a^{-4} -7 z^2 a^{-6} +3 z^2 a^{-8} +4 z^2-3 a^{-2} + a^{-4} - a^{-6} + a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +2 z^9 a^{-1} +3 z^9 a^{-5} +5 z^9 a^{-7} -7 z^8 a^{-2} -19 z^8 a^{-4} -5 z^8 a^{-6} +6 z^8 a^{-8} +z^8-10 z^7 a^{-1} -13 z^7 a^{-3} -21 z^7 a^{-5} -12 z^7 a^{-7} +6 z^7 a^{-9} +19 z^6 a^{-4} -4 z^6 a^{-6} -12 z^6 a^{-8} +5 z^6 a^{-10} -6 z^6+14 z^5 a^{-1} +17 z^5 a^{-3} +28 z^5 a^{-5} +13 z^5 a^{-7} -9 z^5 a^{-9} +3 z^5 a^{-11} +15 z^4 a^{-2} -6 z^4 a^{-4} +10 z^4 a^{-6} +12 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +12 z^4-5 z^3 a^{-1} -2 z^3 a^{-3} -15 z^3 a^{-5} -9 z^3 a^{-7} +6 z^3 a^{-9} -3 z^3 a^{-11} -12 z^2 a^{-2} -7 z^2 a^{-6} -6 z^2 a^{-8} +2 z^2 a^{-10} -z^2 a^{-12} -10 z^2-z a^{-1} -2 z a^{-3} +2 z a^{-5} +2 z a^{-7} -z a^{-9} +3 a^{-2} + a^{-4} + a^{-6} + a^{-8} +3 }[/math] |
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