K12a628
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+5 q^9-11 q^8+17 q^7-24 q^6+29 q^5-30 q^4+28 q^3-22 q^2+15 q-8+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-18 t^2+46 t-61+46 t^{-1} -18 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+z^2+1 }[/math] |
| Determinant | 195 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^6 a^{-6} +2 z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-6} -z^4 a^{-8} -z^4+4 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} -z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +16 z^{10} a^{-6} +9 z^{10} a^{-8} +8 z^9 a^{-3} +8 z^9 a^{-5} +10 z^9 a^{-7} +10 z^9 a^{-9} +8 z^8 a^{-2} -7 z^8 a^{-4} -44 z^8 a^{-6} -24 z^8 a^{-8} +5 z^8 a^{-10} +7 z^7 a^{-1} -3 z^7 a^{-3} -30 z^7 a^{-5} -54 z^7 a^{-7} -33 z^7 a^{-9} +z^7 a^{-11} -4 z^6 a^{-2} +4 z^6 a^{-4} +37 z^6 a^{-6} +11 z^6 a^{-8} -14 z^6 a^{-10} +4 z^6+a z^5-9 z^5 a^{-1} -13 z^5 a^{-3} +22 z^5 a^{-5} +55 z^5 a^{-7} +28 z^5 a^{-9} -2 z^5 a^{-11} -10 z^4 a^{-2} -10 z^4 a^{-4} -9 z^4 a^{-6} +4 z^4 a^{-8} +7 z^4 a^{-10} -6 z^4-a z^3+4 z^3 a^{-1} +12 z^3 a^{-3} +3 z^3 a^{-5} -9 z^3 a^{-7} -5 z^3 a^{-9} +9 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-8} +3 z^2-z a^{-1} -3 z a^{-3} -5 z a^{-5} -4 z a^{-7} -z a^{-9} -2 a^{-2} - a^{-4} }[/math] |
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