K12a9
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-10 q^4+14 q^3-17 q^2+18 q-16+14 q^{-1} -10 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+28 t-35+28 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+2 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-4 a^2 z^2+2 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} +2 z^2+a^4-2 a^2+ a^{-2} -2 a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+4 z^{10} a^{-2} +7 z^{10}+3 a^3 z^9+6 a z^9+9 z^9 a^{-1} +6 z^9 a^{-3} +a^4 z^8-10 a^2 z^8-5 z^8 a^{-2} +6 z^8 a^{-4} -22 z^8-15 a^3 z^7-42 a z^7-43 z^7 a^{-1} -10 z^7 a^{-3} +6 z^7 a^{-5} -5 a^4 z^6+a^2 z^6-6 z^6 a^{-2} -4 z^6 a^{-4} +5 z^6 a^{-6} +9 z^6+24 a^3 z^5+66 a z^5+54 z^5 a^{-1} +4 z^5 a^{-3} -5 z^5 a^{-5} +3 z^5 a^{-7} +8 a^4 z^4+17 a^2 z^4+3 z^4 a^{-2} -8 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} +14 z^4-15 a^3 z^3-37 a z^3-29 z^3 a^{-1} -4 z^3 a^{-3} -3 z^3 a^{-7} -5 a^4 z^2-12 a^2 z^2+2 z^2 a^{-2} +8 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} -9 z^2+3 a^3 z+7 a z+6 z a^{-1} +2 z a^{-3} +z a^{-5} +z a^{-7} +a^4+2 a^2- a^{-2} -2 a^{-4} - a^{-6} +2 }[/math] |
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