K12a532
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+6 q^6-10 q^5+14 q^4-17 q^3+19 q^2-18 q+15-11 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+15 t^2-27 t+33-27 t^{-1} +15 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-9 z^4-3 z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-7 z^4 a^{-2} -2 z^4 a^{-4} +z^4 a^{-6} -2 z^4+2 a^2 z^2-8 z^2 a^{-2} +z^2 a^{-4} +2 z^2 a^{-6} +a^2-3 a^{-2} +2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +6 z^9 a^{-1} +7 z^9 a^{-3} +4 z^9 a^{-5} +3 z^9 a^{-7} +5 z^8 a^{-2} -15 z^8 a^{-4} -11 z^8 a^{-6} +z^8 a^{-8} +8 z^8+8 a z^7-5 z^7 a^{-1} -25 z^7 a^{-3} -27 z^7 a^{-5} -15 z^7 a^{-7} +6 a^2 z^6-32 z^6 a^{-2} -2 z^6 a^{-4} +8 z^6 a^{-6} -5 z^6 a^{-8} -11 z^6+3 a^3 z^5-11 a z^5-9 z^5 a^{-1} +14 z^5 a^{-3} +33 z^5 a^{-5} +24 z^5 a^{-7} +a^4 z^4-7 a^2 z^4+35 z^4 a^{-2} +18 z^4 a^{-4} +4 z^4 a^{-6} +8 z^4 a^{-8} +5 z^4-2 a^3 z^3+8 a z^3+8 z^3 a^{-1} +2 z^3 a^{-3} -9 z^3 a^{-5} -13 z^3 a^{-7} -a^4 z^2+5 a^2 z^2-19 z^2 a^{-2} -9 z^2 a^{-4} -2 z^2 a^{-6} -4 z^2 a^{-8} -2 z^2-2 a z-3 z a^{-1} -2 z a^{-3} +z a^{-7} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math] |
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