K12a710
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-6 q^2+16 q-27+39 q^{-1} -46 q^{-2} +48 q^{-3} -44 q^{-4} +34 q^{-5} -22 q^{-6} +11 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-33 t^2+66 t-81+66 t^{-1} -33 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+z^4-z^2+1 }[/math] |
| Determinant | 299 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-5 z^2 a^6-2 a^6+3 z^6 a^4+7 z^4 a^4+5 z^2 a^4+a^4-z^8 a^2-3 z^6 a^2-4 z^4 a^2-2 z^2 a^2+z^6+z^4+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^5 z^{11}+4 a^3 z^{11}+11 a^6 z^{10}+26 a^4 z^{10}+15 a^2 z^{10}+13 a^7 z^9+29 a^5 z^9+38 a^3 z^9+22 a z^9+9 a^8 z^8-2 a^6 z^8-28 a^4 z^8-a^2 z^8+16 z^8+4 a^9 z^7-21 a^7 z^7-78 a^5 z^7-96 a^3 z^7-37 a z^7+6 z^7 a^{-1} +a^{10} z^6-16 a^8 z^6-28 a^6 z^6-29 a^4 z^6-44 a^2 z^6+z^6 a^{-2} -25 z^6-7 a^9 z^5+16 a^7 z^5+68 a^5 z^5+65 a^3 z^5+15 a z^5-5 z^5 a^{-1} -2 a^{10} z^4+13 a^8 z^4+38 a^6 z^4+44 a^4 z^4+30 a^2 z^4+9 z^4+4 a^9 z^3-6 a^7 z^3-24 a^5 z^3-17 a^3 z^3-3 a z^3+a^{10} z^2-6 a^8 z^2-17 a^6 z^2-15 a^4 z^2-5 a^2 z^2-a^9 z+a^7 z+4 a^5 z+2 a^3 z+a^8+2 a^6+a^4+1 }[/math] |
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