K12a658
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+15 q^5-21 q^4+25 q^3-26 q^2+24 q-18+13 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+38 t-47+38 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4+2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+5 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +2 z^4-2 a^2 z^2+4 z^2 a^{-2} -z^2 a^{-4} -z^2 a^{-6} +2 z^2-a^2+ a^{-2} - a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10}+4 a z^9+3 z^9 a^{-1} +10 z^9 a^{-3} +11 z^9 a^{-5} +3 a^2 z^8-33 z^8 a^{-2} -11 z^8 a^{-4} +11 z^8 a^{-6} -8 z^8+a^3 z^7-10 a z^7-20 z^7 a^{-1} -42 z^7 a^{-3} -25 z^7 a^{-5} +8 z^7 a^{-7} -11 a^2 z^6+41 z^6 a^{-2} +5 z^6 a^{-4} -21 z^6 a^{-6} +4 z^6 a^{-8} -4 a^3 z^5+a z^5+22 z^5 a^{-1} +58 z^5 a^{-3} +28 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4-27 z^4 a^{-2} +3 z^4 a^{-4} +15 z^4 a^{-6} -5 z^4 a^{-8} +2 z^4+5 a^3 z^3+7 a z^3-11 z^3 a^{-1} -31 z^3 a^{-3} -14 z^3 a^{-5} +3 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2+8 z^2 a^{-2} +z^2 a^{-4} -4 z^2 a^{-6} -2 z^2-2 a^3 z-3 a z+z a^{-1} +5 z a^{-3} +3 z a^{-5} +a^2- a^{-2} - a^{-4} +2 }[/math] |
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