K12a700
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-12 q^5+21 q^4-31 q^3+38 q^2-40 q+38-30 q^{-1} +21 q^{-2} -11 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+26 t^2-56 t+73-56 t^{-1} +26 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+4 z^4+z^2+1 }[/math] |
| Determinant | 253 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-9 z^4 a^{-2} +3 z^4 a^{-4} +13 z^4-5 a^2 z^2-11 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +14 z^2-2 a^2-4 a^{-2} + a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +20 z^{10} a^{-2} +9 z^{10} a^{-4} +11 z^{10}+18 a z^9+30 z^9 a^{-1} +22 z^9 a^{-3} +10 z^9 a^{-5} +17 a^2 z^8-27 z^8 a^{-2} -11 z^8 a^{-4} +5 z^8 a^{-6} +6 z^8+10 a^3 z^7-26 a z^7-84 z^7 a^{-1} -76 z^7 a^{-3} -27 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-29 a^2 z^6-27 z^6 a^{-2} -18 z^6 a^{-4} -13 z^6 a^{-6} -55 z^6+a^5 z^5-12 a^3 z^5+11 a z^5+66 z^5 a^{-1} +66 z^5 a^{-3} +22 z^5 a^{-5} -2 z^5 a^{-7} -3 a^4 z^4+28 a^2 z^4+47 z^4 a^{-2} +26 z^4 a^{-4} +10 z^4 a^{-6} +62 z^4-a^5 z^3+8 a^3 z^3+4 a z^3-18 z^3 a^{-1} -19 z^3 a^{-3} -5 z^3 a^{-5} +z^3 a^{-7} -13 a^2 z^2-22 z^2 a^{-2} -8 z^2 a^{-4} -2 z^2 a^{-6} -29 z^2-2 a^3 z-3 a z-z a^{-1} +2 a^2+4 a^{-2} + a^{-4} +6 }[/math] |
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