K12a559
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+5 q^9-11 q^8+18 q^7-26 q^6+31 q^5-33 q^4+31 q^3-24 q^2+17 q-9+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-21 t^2+49 t-63+49 t^{-1} -21 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 211 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-8} -z^4+z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} -z^2+ a^{-2} +2 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +8 z^{10} a^{-4} +17 z^{10} a^{-6} +9 z^{10} a^{-8} +11 z^9 a^{-3} +14 z^9 a^{-5} +13 z^9 a^{-7} +10 z^9 a^{-9} +11 z^8 a^{-2} -3 z^8 a^{-4} -40 z^8 a^{-6} -21 z^8 a^{-8} +5 z^8 a^{-10} +8 z^7 a^{-1} -12 z^7 a^{-3} -48 z^7 a^{-5} -61 z^7 a^{-7} -32 z^7 a^{-9} +z^7 a^{-11} -14 z^6 a^{-2} -15 z^6 a^{-4} +21 z^6 a^{-6} +4 z^6 a^{-8} -14 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} +2 z^5 a^{-3} +47 z^5 a^{-5} +64 z^5 a^{-7} +28 z^5 a^{-9} -2 z^5 a^{-11} +6 z^4 a^{-2} +17 z^4 a^{-4} +8 z^4 a^{-6} +10 z^4 a^{-8} +8 z^4 a^{-10} -5 z^4-a z^3+4 z^3 a^{-1} -z^3 a^{-3} -19 z^3 a^{-5} -19 z^3 a^{-7} -6 z^3 a^{-9} -9 z^2 a^{-4} -10 z^2 a^{-6} -3 z^2 a^{-8} +2 z^2+2 z a^{-3} +2 z a^{-5} -z a^{-7} -z a^{-9} - a^{-2} +2 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
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