K12a217
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+17 q^2-24 q+29-31 q^{-1} +29 q^{-2} -23 q^{-3} +16 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-42 t+53-42 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +5 z^6+3 a^4 z^4-11 a^2 z^4-3 z^4 a^{-2} +11 z^4-a^6 z^2+7 a^4 z^2-14 a^2 z^2-3 z^2 a^{-2} +10 z^2-a^6+4 a^4-5 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+9 a^2 z^{10}+5 z^{10}+6 a^5 z^9+17 a^3 z^9+21 a z^9+10 z^9 a^{-1} +4 a^6 z^8+4 a^4 z^8+3 a^2 z^8+11 z^8 a^{-2} +14 z^8+a^7 z^7-15 a^5 z^7-49 a^3 z^7-48 a z^7-7 z^7 a^{-1} +8 z^7 a^{-3} -13 a^6 z^6-40 a^4 z^6-58 a^2 z^6-14 z^6 a^{-2} +4 z^6 a^{-4} -49 z^6-3 a^7 z^5+7 a^5 z^5+35 a^3 z^5+29 a z^5-7 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +14 a^6 z^4+50 a^4 z^4+71 a^2 z^4+7 z^4 a^{-2} -5 z^4 a^{-4} +47 z^4+3 a^7 z^3+4 a^5 z^3-5 a^3 z^3-3 a z^3+9 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -6 a^6 z^2-23 a^4 z^2-33 a^2 z^2-z^2 a^{-2} +2 z^2 a^{-4} -19 z^2-a^7 z-2 a^5 z-a^3 z-2 a z-3 z a^{-1} -z a^{-3} +a^6+4 a^4+5 a^2+3 }[/math] |
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