K12a868
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+17 q^4-31 q^3+46 q^2-57 q+61-57 q^{-1} +46 q^{-2} -31 q^{-3} +17 q^{-4} -6 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-10 t^3+39 t^2-84 t+109-84 t^{-1} +39 t^{-2} -10 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^6-z^4-2 z^2+1 }[/math] |
| Determinant | 377 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +2 z^6+a^4 z^4-2 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} +z^4+a^2 z^2+z^2 a^{-2} -4 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 8 a z^{11}+8 z^{11} a^{-1} +23 a^2 z^{10}+23 z^{10} a^{-2} +46 z^{10}+27 a^3 z^9+45 a z^9+45 z^9 a^{-1} +27 z^9 a^{-3} +17 a^4 z^8-18 a^2 z^8-18 z^8 a^{-2} +17 z^8 a^{-4} -70 z^8+6 a^5 z^7-45 a^3 z^7-124 a z^7-124 z^7 a^{-1} -45 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-23 a^4 z^6-24 a^2 z^6-24 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} -4 a^5 z^5+25 a^3 z^5+82 a z^5+82 z^5 a^{-1} +25 z^5 a^{-3} -4 z^5 a^{-5} +9 a^4 z^4+18 a^2 z^4+18 z^4 a^{-2} +9 z^4 a^{-4} +18 z^4-6 a^3 z^3-12 a z^3-12 z^3 a^{-1} -6 z^3 a^{-3} -a^4 z^2+2 a^2 z^2+2 z^2 a^{-2} -z^2 a^{-4} +6 z^2-2 a z-2 z a^{-1} -2 a^2-2 a^{-2} -3 }[/math] |
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