K12a491
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-16 q^3+22 q^2-27 q+28-25 q^{-1} +20 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-42 t+61-42 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4-4 z^2+1 }[/math] |
| Determinant | 177 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-2 a^4+3 z^4 a^2+3 z^2 a^2+2 a^2-z^6+1-z^6 a^{-2} -2 z^4 a^{-2} -5 z^2 a^{-2} -3 a^{-2} +z^4 a^{-4} +z^2 a^{-4} +2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+7 z^{10} a^{-2} +11 z^{10}+4 a^3 z^9+4 a z^9+11 z^9 a^{-1} +11 z^9 a^{-3} +4 a^4 z^8-4 a^2 z^8-10 z^8 a^{-2} +9 z^8 a^{-4} -27 z^8+3 a^5 z^7-10 a z^7-42 z^7 a^{-1} -31 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-5 a^4 z^6+8 a^2 z^6-8 z^6 a^{-2} -24 z^6 a^{-4} +z^6 a^{-6} +31 z^6-8 a^5 z^5-14 a^3 z^5+8 a z^5+53 z^5 a^{-1} +31 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4-5 a^4 z^4-18 a^2 z^4+25 z^4 a^{-2} +19 z^4 a^{-4} -2 z^4 a^{-6} -12 z^4+7 a^5 z^3+12 a^3 z^3-2 a z^3-22 z^3 a^{-1} -14 z^3 a^{-3} +z^3 a^{-5} +3 a^6 z^2+8 a^4 z^2+10 a^2 z^2-15 z^2 a^{-2} -9 z^2 a^{-4} -z^2-2 a^5 z-3 a^3 z-a z+3 z a^{-1} +3 z a^{-3} -a^6-2 a^4-2 a^2+3 a^{-2} +2 a^{-4} +1 }[/math] |
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