K12a834
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+8 q^6-14 q^5+20 q^4-24 q^3+27 q^2-25 q+21-15 q^{-1} +9 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+19 t^2-39 t+49-39 t^{-1} +19 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-5 z^4+z^2+1 }[/math] |
| Determinant | 173 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-5 z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-6} -z^4+a^2 z^2-4 z^2 a^{-2} +2 z^2 a^{-4} +z^2 a^{-6} +z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +12 z^{10} a^{-4} +5 z^{10} a^{-6} +13 z^9 a^{-1} +15 z^9 a^{-3} +6 z^9 a^{-5} +4 z^9 a^{-7} +2 z^8 a^{-2} -33 z^8 a^{-4} -18 z^8 a^{-6} +z^8 a^{-8} +16 z^8+14 a z^7-18 z^7 a^{-1} -60 z^7 a^{-3} -46 z^7 a^{-5} -18 z^7 a^{-7} +9 a^2 z^6-44 z^6 a^{-2} +10 z^6 a^{-4} +15 z^6 a^{-6} -4 z^6 a^{-8} -26 z^6+4 a^3 z^5-18 a z^5-5 z^5 a^{-1} +55 z^5 a^{-3} +64 z^5 a^{-5} +26 z^5 a^{-7} +a^4 z^4-7 a^2 z^4+43 z^4 a^{-2} +21 z^4 a^{-4} +4 z^4 a^{-6} +5 z^4 a^{-8} +13 z^4-a^3 z^3+8 a z^3+6 z^3 a^{-1} -17 z^3 a^{-3} -26 z^3 a^{-5} -12 z^3 a^{-7} +2 a^2 z^2-15 z^2 a^{-2} -11 z^2 a^{-4} -5 z^2 a^{-6} -2 z^2 a^{-8} -5 z^2-a z-z a^{-1} +2 z a^{-3} +2 z a^{-5} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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