K12a667
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+11 q^4-15 q^3+18 q^2-18 q+18-13 q^{-1} +9 q^{-2} -5 q^{-3} +2 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+15 t^2-23 t+27-23 t^{-1} +15 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+13 z^4+6 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} +6 z^6-5 a^2 z^4+8 z^4 a^{-2} -4 z^4 a^{-4} +14 z^4-8 a^2 z^2+4 z^2 a^{-2} -5 z^2 a^{-4} +15 z^2-4 a^2-2 a^{-4} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +3 z^{10} a^{-4} +3 z^{10}+4 a z^9+5 z^9 a^{-1} +5 z^9 a^{-3} +4 z^9 a^{-5} +4 a^2 z^8-16 z^8 a^{-2} -5 z^8 a^{-4} +3 z^8 a^{-6} -4 z^8+3 a^3 z^7-8 a z^7-21 z^7 a^{-1} -23 z^7 a^{-3} -12 z^7 a^{-5} +z^7 a^{-7} +2 a^4 z^6-9 a^2 z^6+13 z^6 a^{-2} -5 z^6 a^{-4} -11 z^6 a^{-6} -4 z^6+a^5 z^5-5 a^3 z^5+6 a z^5+26 z^5 a^{-1} +25 z^5 a^{-3} +7 z^5 a^{-5} -4 z^5 a^{-7} -4 a^4 z^4+13 a^2 z^4-4 z^4 a^{-2} +3 z^4 a^{-4} +11 z^4 a^{-6} +21 z^4-3 a^5 z^3+2 a^3 z^3+7 a z^3-7 z^3 a^{-1} -15 z^3 a^{-3} -z^3 a^{-5} +5 z^3 a^{-7} +a^4 z^2-11 a^2 z^2+3 z^2 a^{-4} -3 z^2 a^{-6} -18 z^2+2 a^5 z-a^3 z-6 a z-2 z a^{-1} +4 z a^{-3} +z a^{-5} -2 z a^{-7} +4 a^2-2 a^{-4} +7 }[/math] |
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