K12a171
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+16 q^4-23 q^3+29 q^2-31 q+29-24 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+18 t^2-46 t+63-46 t^{-1} +18 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-6 z^4 a^{-2} +3 z^4 a^{-4} +z^4-a^4 z^2+a^2 z^2-10 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +4 z^2-5 a^{-2} +4 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +9 z^{10} a^{-2} +4 z^{10} a^{-4} +5 z^{10}+10 a z^9+21 z^9 a^{-1} +17 z^9 a^{-3} +6 z^9 a^{-5} +11 a^2 z^8+3 z^8 a^{-2} +4 z^8 a^{-4} +4 z^8 a^{-6} +14 z^8+8 a^3 z^7-7 a z^7-48 z^7 a^{-1} -49 z^7 a^{-3} -15 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-14 a^2 z^6-58 z^6 a^{-2} -40 z^6 a^{-4} -13 z^6 a^{-6} -49 z^6+a^5 z^5-10 a^3 z^5-7 a z^5+29 z^5 a^{-1} +35 z^5 a^{-3} +7 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+7 a^2 z^4+71 z^4 a^{-2} +50 z^4 a^{-4} +14 z^4 a^{-6} +47 z^4-a^5 z^3+5 a^3 z^3+9 a z^3-3 z^3 a^{-1} -5 z^3 a^{-3} +4 z^3 a^{-5} +3 z^3 a^{-7} +2 a^4 z^2-a^2 z^2-33 z^2 a^{-2} -23 z^2 a^{-4} -6 z^2 a^{-6} -19 z^2-a^3 z-3 a z-2 z a^{-1} -z a^{-3} -2 z a^{-5} -z a^{-7} +5 a^{-2} +4 a^{-4} + a^{-6} +3 }[/math] |
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