K12a1146
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+5 q^6-9 q^5+12 q^4-16 q^3+18 q^2-17 q+15-11 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+14 t^2-25 t+31-25 t^{-1} +14 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-10 z^4-5 z^2+1 }[/math] |
| Determinant | 117 |
| 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} -3 z^4 a^{-4} +z^4 a^{-6} -2 z^4+2 a^2 z^2-7 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +a^2- a^{-2} -2 a^{-4} +2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +5 z^{10} a^{-4} +2 z^{10} a^{-6} +6 z^9 a^{-1} +4 z^9 a^{-3} +2 z^9 a^{-7} +z^8 a^{-2} -15 z^8 a^{-4} -7 z^8 a^{-6} +z^8 a^{-8} +8 z^8+8 a z^7-8 z^7 a^{-1} -13 z^7 a^{-3} -7 z^7 a^{-5} -10 z^7 a^{-7} +6 a^2 z^6-15 z^6 a^{-2} +14 z^6 a^{-4} +5 z^6 a^{-6} -6 z^6 a^{-8} -12 z^6+3 a^3 z^5-11 a z^5+2 z^5 a^{-1} +z^5 a^{-3} +z^5 a^{-5} +16 z^5 a^{-7} +a^4 z^4-7 a^2 z^4+13 z^4 a^{-2} -14 z^4 a^{-4} +12 z^4 a^{-8} +7 z^4-2 a^3 z^3+7 a z^3-3 z^3 a^{-1} +6 z^3 a^{-3} +9 z^3 a^{-5} -9 z^3 a^{-7} -a^4 z^2+5 a^2 z^2-9 z^2 a^{-2} +11 z^2 a^{-4} +4 z^2 a^{-6} -8 z^2 a^{-8} -2 z^2-3 z a^{-3} -z a^{-5} +2 z a^{-7} -a^2+ a^{-2} -2 a^{-4} -2 a^{-6} +1 }[/math] |
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