K12a1288
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+5 q^4-10 q^3+14 q^2-17 q+19-17 q^{-1} +14 q^{-2} -10 q^{-3} +5 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-7 t^3+14 t^2-21 t+25-21 t^{-1} +14 t^{-2} -7 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-18 z^6-18 z^4-5 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -9 z^8+7 a^2 z^6+7 z^6 a^{-2} -32 z^6+18 a^2 z^4+18 z^4 a^{-2} -54 z^4+18 a^2 z^2+18 z^2 a^{-2} -41 z^2+5 a^2+5 a^{-2} -9 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+4 a^3 z^9+3 a z^9+3 z^9 a^{-1} +4 z^9 a^{-3} +3 a^4 z^8-9 a^2 z^8-9 z^8 a^{-2} +3 z^8 a^{-4} -24 z^8+2 a^5 z^7-14 a^3 z^7-16 a z^7-16 z^7 a^{-1} -14 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-8 a^4 z^6+20 a^2 z^6+20 z^6 a^{-2} -8 z^6 a^{-4} +z^6 a^{-6} +58 z^6-6 a^5 z^5+26 a^3 z^5+34 a z^5+34 z^5 a^{-1} +26 z^5 a^{-3} -6 z^5 a^{-5} -4 a^6 z^4+7 a^4 z^4-26 a^2 z^4-26 z^4 a^{-2} +7 z^4 a^{-4} -4 z^4 a^{-6} -74 z^4+4 a^5 z^3-24 a^3 z^3-27 a z^3-27 z^3 a^{-1} -24 z^3 a^{-3} +4 z^3 a^{-5} +4 a^6 z^2-4 a^4 z^2+17 a^2 z^2+17 z^2 a^{-2} -4 z^2 a^{-4} +4 z^2 a^{-6} +50 z^2+4 a^3 z+7 a z+7 z a^{-1} +4 z a^{-3} -5 a^2-5 a^{-2} -9 }[/math] |
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