K12a505
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+8 q-14+22 q^{-1} -26 q^{-2} +29 q^{-3} -27 q^{-4} +22 q^{-5} -16 q^{-6} +9 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-21 t^2+39 t-47+39 t^{-1} -21 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-7 z^2 a^6-4 a^6+3 z^6 a^4+11 z^4 a^4+13 z^2 a^4+4 a^4-z^8 a^2-5 z^6 a^2-10 z^4 a^2-7 z^2 a^2+z^6+3 z^4+2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+4 a^6 z^{10}+8 a^4 z^{10}+4 a^2 z^{10}+7 a^7 z^9+15 a^5 z^9+15 a^3 z^9+7 a z^9+7 a^8 z^8+7 a^6 z^8-a^4 z^8+6 a^2 z^8+7 z^8+4 a^9 z^7-8 a^7 z^7-37 a^5 z^7-41 a^3 z^7-12 a z^7+4 z^7 a^{-1} +a^{10} z^6-14 a^8 z^6-31 a^6 z^6-34 a^4 z^6-37 a^2 z^6+z^6 a^{-2} -18 z^6-9 a^9 z^5-5 a^7 z^5+34 a^5 z^5+42 a^3 z^5+2 a z^5-10 z^5 a^{-1} -2 a^{10} z^4+7 a^8 z^4+31 a^6 z^4+54 a^4 z^4+49 a^2 z^4-2 z^4 a^{-2} +15 z^4+6 a^9 z^3+5 a^7 z^3-15 a^5 z^3-16 a^3 z^3+3 a z^3+5 z^3 a^{-1} +a^{10} z^2-2 a^8 z^2-17 a^6 z^2-28 a^4 z^2-20 a^2 z^2-6 z^2-a^9 z-2 a^7 z+2 a^5 z+4 a^3 z+a z+a^8+4 a^6+4 a^4 }[/math] |
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