K12a254
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+5 q^{10}-9 q^9+12 q^8-14 q^7+15 q^6-13 q^5+11 q^4-7 q^3+4 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+13 t^2-21 t+23-21 t^{-1} +13 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-5 z^4+4 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -3 z^4 a^{-4} -z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -2 z^2 a^{-4} +4 z^2 a^{-6} -3 z^2 a^{-8} +2 z^2 a^{-10} + a^{-2} - a^{-4} +3 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} -z^9 a^{-7} +z^9 a^{-9} +4 z^9 a^{-11} +2 z^8 a^{-4} -7 z^8 a^{-6} -23 z^8 a^{-8} -10 z^8 a^{-10} +4 z^8 a^{-12} +2 z^7 a^{-3} -4 z^7 a^{-5} -4 z^7 a^{-7} -13 z^7 a^{-9} -12 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -4 z^6 a^{-4} +16 z^6 a^{-6} +49 z^6 a^{-8} +15 z^6 a^{-10} -12 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +z^5 a^{-5} +18 z^5 a^{-7} +29 z^5 a^{-9} +9 z^5 a^{-11} -10 z^5 a^{-13} -4 z^4 a^{-2} -2 z^4 a^{-4} -20 z^4 a^{-6} -43 z^4 a^{-8} -11 z^4 a^{-10} +7 z^4 a^{-12} -3 z^4 a^{-14} +6 z^3 a^{-3} +z^3 a^{-5} -17 z^3 a^{-7} -18 z^3 a^{-9} +z^3 a^{-11} +7 z^3 a^{-13} +4 z^2 a^{-2} +4 z^2 a^{-4} +12 z^2 a^{-6} +17 z^2 a^{-8} +4 z^2 a^{-10} +z^2 a^{-14} -z a^{-3} -z a^{-5} +4 z a^{-7} +2 z a^{-9} -3 z a^{-11} -z a^{-13} - a^{-2} - a^{-4} -3 a^{-6} -2 a^{-8} }[/math] |
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