K12a683
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+6 q^8-10 q^7+15 q^6-17 q^5+17 q^4-17 q^3+13 q^2-9 q+6-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+16 t^2-22 t+25-22 t^{-1} +16 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-6 z^4-5 z^2+1 }[/math] |
| Determinant | 117 |
| 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} +9 z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-8} +z^4-12 z^2 a^{-2} +8 z^2 a^{-4} -8 z^2 a^{-6} +3 z^2 a^{-8} +4 z^2-5 a^{-2} +2 a^{-4} - a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +6 z^{10} a^{-4} +4 z^{10} a^{-6} +2 z^9 a^{-1} +2 z^9 a^{-3} +8 z^9 a^{-5} +8 z^9 a^{-7} -5 z^8 a^{-2} -18 z^8 a^{-4} -3 z^8 a^{-6} +9 z^8 a^{-8} +z^8-9 z^7 a^{-1} -17 z^7 a^{-3} -37 z^7 a^{-5} -22 z^7 a^{-7} +7 z^7 a^{-9} -6 z^6 a^{-2} +9 z^6 a^{-4} -18 z^6 a^{-6} -22 z^6 a^{-8} +5 z^6 a^{-10} -6 z^6+11 z^5 a^{-1} +14 z^5 a^{-3} +41 z^5 a^{-5} +25 z^5 a^{-7} -10 z^5 a^{-9} +3 z^5 a^{-11} +21 z^4 a^{-2} +2 z^4 a^{-4} +23 z^4 a^{-6} +23 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +13 z^4-z^3 a^{-1} +7 z^3 a^{-3} -15 z^3 a^{-5} -15 z^3 a^{-7} +5 z^3 a^{-9} -3 z^3 a^{-11} -16 z^2 a^{-2} -z^2 a^{-4} -7 z^2 a^{-6} -8 z^2 a^{-8} +z^2 a^{-10} -z^2 a^{-12} -12 z^2-3 z a^{-1} -8 z a^{-3} -2 z a^{-5} +3 z a^{-7} +5 a^{-2} +2 a^{-4} + a^{-6} + a^{-8} +4 }[/math] |
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