K12a531
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-13 q^6+18 q^5-22 q^4+24 q^3-22 q^2+18 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-18 t^2+30 t-35+30 t^{-1} -18 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-10 z^4-2 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-9 z^4 a^{-2} -9 z^4 a^{-4} +4 z^4 a^{-6} +4 z^4-6 z^2 a^{-2} -6 z^2 a^{-4} +5 z^2 a^{-6} +5 z^2- a^{-2} - a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +5 z^9 a^{-1} +8 z^9 a^{-3} +9 z^9 a^{-5} +6 z^9 a^{-7} +2 z^8 a^{-2} -14 z^8 a^{-4} -6 z^8 a^{-6} +5 z^8 a^{-8} +5 z^8+3 a z^7-9 z^7 a^{-1} -23 z^7 a^{-3} -30 z^7 a^{-5} -16 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-18 z^6 a^{-2} +16 z^6 a^{-4} +7 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -13 z^6-8 a z^5+3 z^5 a^{-1} +26 z^5 a^{-3} +45 z^5 a^{-5} +22 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+24 z^4 a^{-2} -11 z^4 a^{-4} -9 z^4 a^{-6} +8 z^4 a^{-8} -3 z^4 a^{-10} +12 z^4+5 a z^3+z^3 a^{-1} -11 z^3 a^{-3} -31 z^3 a^{-5} -19 z^3 a^{-7} +5 z^3 a^{-9} +2 a^2 z^2-11 z^2 a^{-2} +7 z^2 a^{-4} +4 z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} -8 z^2-a z-z a^{-1} +3 z a^{-3} +7 z a^{-5} +4 z a^{-7} + a^{-2} - a^{-4} - a^{-6} +2 }[/math] |
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