K12a1155
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-5 q^{11}+13 q^{10}-24 q^9+34 q^8-42 q^7+44 q^6-40 q^5+33 q^4-21 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+28 t^2-63 t+81-63 t^{-1} +28 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-2 z^4+4 z^2+1 }[/math] |
| Determinant | 273 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} +2 z^2 a^{-8} +2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-7} +4 z^{11} a^{-9} +11 z^{10} a^{-6} +24 z^{10} a^{-8} +13 z^{10} a^{-10} +13 z^9 a^{-5} +23 z^9 a^{-7} +27 z^9 a^{-9} +17 z^9 a^{-11} +9 z^8 a^{-4} -8 z^8 a^{-6} -39 z^8 a^{-8} -10 z^8 a^{-10} +12 z^8 a^{-12} +4 z^7 a^{-3} -24 z^7 a^{-5} -69 z^7 a^{-7} -78 z^7 a^{-9} -32 z^7 a^{-11} +5 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -15 z^6 a^{-6} +9 z^6 a^{-8} -16 z^6 a^{-10} -21 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +20 z^5 a^{-5} +69 z^5 a^{-7} +70 z^5 a^{-9} +21 z^5 a^{-11} -7 z^5 a^{-13} -2 z^4 a^{-2} +14 z^4 a^{-4} +24 z^4 a^{-6} +11 z^4 a^{-8} +15 z^4 a^{-10} +11 z^4 a^{-12} -z^4 a^{-14} +3 z^3 a^{-3} -9 z^3 a^{-5} -32 z^3 a^{-7} -30 z^3 a^{-9} -8 z^3 a^{-11} +2 z^3 a^{-13} +z^2 a^{-2} -8 z^2 a^{-4} -11 z^2 a^{-6} -4 z^2 a^{-8} -4 z^2 a^{-10} -2 z^2 a^{-12} +z a^{-5} +7 z a^{-7} +7 z a^{-9} +z a^{-11} +2 a^{-4} - a^{-8} }[/math] |
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