K12a912
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+6 q^6-9 q^5+13 q^4-16 q^3+17 q^2-17 q+14-10 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+12 t^2-26 t+35-26 t^{-1} +12 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-6 z^4-5 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-2 z^4 a^{-2} -3 z^4 a^{-4} +z^4 a^{-6} -3 z^4+2 a^2 z^2-2 z^2 a^{-2} -3 z^2 a^{-4} +2 z^2 a^{-6} -4 z^2+2 a^2- a^{-2} + a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +9 z^{10} a^{-4} +4 z^{10} a^{-6} +7 z^9 a^{-1} +z^9 a^{-3} -3 z^9 a^{-5} +3 z^9 a^{-7} -12 z^8 a^{-2} -39 z^8 a^{-4} -19 z^8 a^{-6} +z^8 a^{-8} +7 z^8+7 a z^7-17 z^7 a^{-1} -24 z^7 a^{-3} -15 z^7 a^{-5} -15 z^7 a^{-7} +6 a^2 z^6+5 z^6 a^{-2} +52 z^6 a^{-4} +27 z^6 a^{-6} -5 z^6 a^{-8} -9 z^6+3 a^3 z^5-8 a z^5+19 z^5 a^{-1} +36 z^5 a^{-3} +28 z^5 a^{-5} +22 z^5 a^{-7} +a^4 z^4-8 a^2 z^4+5 z^4 a^{-2} -27 z^4 a^{-4} -16 z^4 a^{-6} +7 z^4 a^{-8} -2 a^3 z^3+2 a z^3-17 z^3 a^{-1} -21 z^3 a^{-3} -11 z^3 a^{-5} -11 z^3 a^{-7} -a^4 z^2+6 a^2 z^2-8 z^2 a^{-2} +5 z^2 a^{-4} +6 z^2 a^{-6} -3 z^2 a^{-8} +3 z^2+a z+6 z a^{-1} +5 z a^{-3} +z a^{-5} +z a^{-7} -2 a^2+ a^{-2} - a^{-6} -1 }[/math] |
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