K12a665
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-16 q^6+24 q^5-29 q^4+31 q^3-29 q^2+23 q-16+9 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-17 t^2+47 t-63+47 t^{-1} -17 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-5 z^4-3 z^2+1 }[/math] |
| Determinant | 195 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} -z^4 a^{-2} -2 z^4 a^{-6} -2 z^4+a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} -z^2+a^2-3 a^{-2} +2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10} a^{-6} +7 z^9 a^{-1} +11 z^9 a^{-3} +14 z^9 a^{-5} +10 z^9 a^{-7} +2 z^8 a^{-2} -20 z^8 a^{-4} -8 z^8 a^{-6} +8 z^8 a^{-8} +6 z^8+3 a z^7-10 z^7 a^{-1} -30 z^7 a^{-3} -46 z^7 a^{-5} -25 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-22 z^6 a^{-2} +3 z^6 a^{-4} -9 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -12 z^6-6 a z^5+4 z^5 a^{-1} +29 z^5 a^{-3} +51 z^5 a^{-5} +23 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4+28 z^4 a^{-2} +20 z^4 a^{-4} +21 z^4 a^{-6} +15 z^4 a^{-8} -2 z^4 a^{-10} +9 z^4+3 a z^3-6 z^3 a^{-1} -15 z^3 a^{-3} -18 z^3 a^{-5} -9 z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2-19 z^2 a^{-2} -14 z^2 a^{-4} -8 z^2 a^{-6} -5 z^2 a^{-8} -5 z^2+3 z a^{-1} +4 z a^{-3} +2 z a^{-5} +z a^{-7} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math] |
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