K12a481
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+5 q^3-9 q^2+13 q-16+18 q^{-1} -18 q^{-2} +15 q^{-3} -11 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+28 t-33+28 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-6 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4+z^6 a^2+z^4 a^2-2 z^2 a^2-2 a^2+z^6+2 z^4+2 z^2+3-2 z^4 a^{-2} -5 z^2 a^{-2} -3 a^{-2} +z^2 a^{-4} +2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+2 z^{10} a^{-2} +5 z^{10}+6 a^3 z^9+5 a z^9+z^9 a^{-1} +2 z^9 a^{-3} +8 a^4 z^8+3 a^2 z^8-6 z^8 a^{-2} +z^8 a^{-4} -12 z^8+8 a^5 z^7-6 a^3 z^7-17 a z^7-13 z^7 a^{-1} -10 z^7 a^{-3} +6 a^6 z^6-11 a^4 z^6-24 a^2 z^6-2 z^6 a^{-2} -6 z^6 a^{-4} -3 z^6+3 a^7 z^5-11 a^5 z^5-6 a^3 z^5+5 a z^5+13 z^5 a^{-1} +16 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+4 a^4 z^4+24 a^2 z^4+17 z^4 a^{-2} +12 z^4 a^{-4} +17 z^4-2 a^7 z^3+8 a^5 z^3+5 a^3 z^3+4 a z^3-9 z^3 a^{-3} -a^8 z^2+5 a^6 z^2-12 a^2 z^2-13 z^2 a^{-2} -9 z^2 a^{-4} -10 z^2-2 a^5 z-a^3 z-a z-z a^{-1} +z a^{-3} -a^6+2 a^2+3 a^{-2} +2 a^{-4} +3 }[/math] |
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