K12a606
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-15 q^3+21 q^2-25 q+27-24 q^{-1} +19 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-38 t+49-38 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4-2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-2 a^2 z^4-z^4 a^{-2} +z^4 a^{-4} -5 z^4+2 a^4 z^2-2 a^2 z^2+z^2 a^{-2} +z^2 a^{-4} -4 z^2+a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+6 z^{10} a^{-2} +11 z^{10}+6 a^3 z^9+6 a z^9+8 z^9 a^{-1} +8 z^9 a^{-3} +5 a^4 z^8-9 a^2 z^8-10 z^8 a^{-2} +7 z^8 a^{-4} -31 z^8+3 a^5 z^7-14 a^3 z^7-29 a z^7-33 z^7 a^{-1} -17 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-12 a^4 z^6+5 a^2 z^6+6 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} +40 z^6-8 a^5 z^5+13 a^3 z^5+47 a z^5+46 z^5 a^{-1} +11 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4+8 a^4 z^4+4 a^2 z^4-5 z^4 a^{-2} +6 z^4 a^{-4} -2 z^4 a^{-6} -20 z^4+5 a^5 z^3-8 a^3 z^3-27 a z^3-25 z^3 a^{-1} -7 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2-4 a^4 z^2-5 a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} +z^2 a^{-6} +6 z^2-a^5 z+a^3 z+5 a z+5 z a^{-1} +2 z a^{-3} +a^4+a^2- a^{-2} }[/math] |
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