K12a426
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+15 q^4-25 q^3+35 q^2-42 q+44-39 q^{-1} +31 q^{-2} -20 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-60 t+77-60 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^4+1 }[/math] |
| Determinant | 273 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +9 z^4+2 a^4 z^2-8 a^2 z^2-3 z^2 a^{-2} +9 z^2+a^4-3 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+12 z^{10} a^{-2} +20 z^{10}+10 a^3 z^9+23 a z^9+32 z^9 a^{-1} +19 z^9 a^{-3} +8 a^4 z^8+5 a^2 z^8+3 z^8 a^{-2} +15 z^8 a^{-4} -15 z^8+4 a^5 z^7-10 a^3 z^7-50 a z^7-73 z^7 a^{-1} -31 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-14 a^4 z^6-34 a^2 z^6-44 z^6 a^{-2} -25 z^6 a^{-4} +z^6 a^{-6} -37 z^6-8 a^5 z^5-6 a^3 z^5+22 a z^5+33 z^5 a^{-1} +7 z^5 a^{-3} -6 z^5 a^{-5} -2 a^6 z^4+10 a^4 z^4+38 a^2 z^4+30 z^4 a^{-2} +8 z^4 a^{-4} +48 z^4+6 a^5 z^3+14 a^3 z^3+13 a z^3+10 z^3 a^{-1} +5 z^3 a^{-3} +a^6 z^2-4 a^4 z^2-18 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -20 z^2-2 a^5 z-6 a^3 z-8 a z-6 z a^{-1} -2 z a^{-3} +a^4+3 a^2+ a^{-2} +4 }[/math] |
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