K12a699
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-13 q^3+24 q^2-33 q+40-42 q^{-1} +38 q^{-2} -30 q^{-3} +20 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-57 t+73-57 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^2+1 }[/math] |
| Determinant | 261 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-9 a^2 z^4-2 z^4 a^{-2} +8 z^4-a^6 z^2+6 a^4 z^2-11 a^2 z^2-2 z^2 a^{-2} +7 z^2-a^6+4 a^4-5 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+7 a^4 z^{10}+20 a^2 z^{10}+13 z^{10}+7 a^5 z^9+18 a^3 z^9+34 a z^9+23 z^9 a^{-1} +4 a^6 z^8-5 a^4 z^8-26 a^2 z^8+22 z^8 a^{-2} +5 z^8+a^7 z^7-16 a^5 z^7-61 a^3 z^7-92 a z^7-35 z^7 a^{-1} +13 z^7 a^{-3} -12 a^6 z^6-24 a^4 z^6-28 a^2 z^6-33 z^6 a^{-2} +5 z^6 a^{-4} -54 z^6-3 a^7 z^5+9 a^5 z^5+54 a^3 z^5+72 a z^5+17 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4+38 a^4 z^4+54 a^2 z^4+19 z^4 a^{-2} -2 z^4 a^{-4} +50 z^4+3 a^7 z^3+a^5 z^3-18 a^3 z^3-24 a z^3-5 z^3 a^{-1} +3 z^3 a^{-3} -6 a^6 z^2-21 a^4 z^2-29 a^2 z^2-5 z^2 a^{-2} -19 z^2-a^7 z-a^5 z+3 a^3 z+4 a z+z a^{-1} +a^6+4 a^4+5 a^2+3 }[/math] |
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