K12a567
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+6 q^6-14 q^5+23 q^4-32 q^3+38 q^2-39 q+36-28 q^{-1} +18 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+31 t^2-50 t+59-50 t^{-1} +31 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+4 z^6-z^4-2 z^2+1 }[/math] |
| Determinant | 249 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+2 z^6 a^{-2} -z^6 a^{-4} +4 z^6-3 a^2 z^4-4 z^4 a^{-2} -z^4 a^{-4} +7 z^4-2 a^2 z^2-10 z^2 a^{-2} +3 z^2 a^{-4} +7 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +23 z^{10} a^{-2} +12 z^{10} a^{-4} +11 z^{10}+14 a z^9+21 z^9 a^{-1} +20 z^9 a^{-3} +13 z^9 a^{-5} +12 a^2 z^8-46 z^8 a^{-2} -22 z^8 a^{-4} +6 z^8 a^{-6} -6 z^8+8 a^3 z^7-18 a z^7-69 z^7 a^{-1} -79 z^7 a^{-3} -35 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-14 a^2 z^6+4 z^6 a^{-2} -6 z^6 a^{-4} -13 z^6 a^{-6} -21 z^6+a^5 z^5-9 a^3 z^5+5 a z^5+56 z^5 a^{-1} +65 z^5 a^{-3} +23 z^5 a^{-5} -z^5 a^{-7} -5 a^4 z^4+5 a^2 z^4+31 z^4 a^{-2} +17 z^4 a^{-4} +5 z^4 a^{-6} +29 z^4-a^5 z^3+4 a^3 z^3+7 a z^3-9 z^3 a^{-1} -11 z^3 a^{-3} +2 a^4 z^2+a^2 z^2-21 z^2 a^{-2} -7 z^2 a^{-4} +2 z^2 a^{-6} -13 z^2-a^3 z-3 a z-3 z a^{-1} -3 z a^{-3} -2 z a^{-5} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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