K12a568
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-15 q^9+20 q^8-24 q^7+25 q^6-22 q^5+17 q^4-11 q^3+6 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-35 t+43-35 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4+z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -2 z^4 a^{-4} -5 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} +2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +4 z^9 a^{-5} +8 z^9 a^{-7} +11 z^9 a^{-9} +7 z^9 a^{-11} +3 z^8 a^{-4} -2 z^8 a^{-6} -10 z^8 a^{-8} +2 z^8 a^{-10} +7 z^8 a^{-12} +2 z^7 a^{-3} -9 z^7 a^{-5} -26 z^7 a^{-7} -30 z^7 a^{-9} -11 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -5 z^6 a^{-4} -3 z^6 a^{-6} -19 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -5 z^5 a^{-3} +13 z^5 a^{-5} +39 z^5 a^{-7} +29 z^5 a^{-9} -z^5 a^{-11} -9 z^5 a^{-13} -4 z^4 a^{-2} -z^4 a^{-4} +8 z^4 a^{-6} +12 z^4 a^{-8} +16 z^4 a^{-10} +7 z^4 a^{-12} -2 z^4 a^{-14} +2 z^3 a^{-3} -13 z^3 a^{-5} -24 z^3 a^{-7} -11 z^3 a^{-9} +3 z^3 a^{-11} +5 z^3 a^{-13} +5 z^2 a^{-2} +3 z^2 a^{-4} -5 z^2 a^{-6} -4 z^2 a^{-8} -4 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +z a^{-3} +3 z a^{-5} +5 z a^{-7} +3 z a^{-9} -z a^{-11} -z a^{-13} -2 a^{-2} - a^{-4} }[/math] |
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