K12a1050
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-12 q^5+23 q^4-34 q^3+42 q^2-46 q+43-35 q^{-1} +25 q^{-2} -13 q^{-3} +5 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-63 t+83-63 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^4-3 z^2+1 }[/math] |
| Determinant | 285 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +4 z^6-2 a^2 z^4-8 z^4 a^{-2} +3 z^4 a^{-4} +8 z^4-2 a^2 z^2-9 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +5 z^2+a^2-3 a^{-2} +2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +26 z^{10} a^{-2} +10 z^{10} a^{-4} +16 z^{10}+26 a z^9+40 z^9 a^{-1} +24 z^9 a^{-3} +10 z^9 a^{-5} +23 a^2 z^8-39 z^8 a^{-2} -11 z^8 a^{-4} +5 z^8 a^{-6} +13 a^3 z^7-43 a z^7-119 z^7 a^{-1} -89 z^7 a^{-3} -25 z^7 a^{-5} +z^7 a^{-7} +5 a^4 z^6-34 a^2 z^6-30 z^6 a^{-2} -24 z^6 a^{-4} -13 z^6 a^{-6} -58 z^6+a^5 z^5-11 a^3 z^5+26 a z^5+104 z^5 a^{-1} +88 z^5 a^{-3} +20 z^5 a^{-5} -2 z^5 a^{-7} -2 a^4 z^4+20 a^2 z^4+68 z^4 a^{-2} +40 z^4 a^{-4} +11 z^4 a^{-6} +61 z^4+2 a^3 z^3-9 a z^3-39 z^3 a^{-1} -36 z^3 a^{-3} -7 z^3 a^{-5} +z^3 a^{-7} -5 a^2 z^2-32 z^2 a^{-2} -19 z^2 a^{-4} -3 z^2 a^{-6} -21 z^2+2 a z+8 z a^{-1} +7 z a^{-3} +z a^{-5} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math] |
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