K12a664
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-15 q^7+21 q^6-25 q^5+26 q^4-24 q^3+19 q^2-13 q+8-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+22 t^2-34 t+39-34 t^{-1} +22 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-6 z^4-2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +4 z^6 a^{-4} -2 z^6 a^{-6} -7 z^4 a^{-2} +5 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +z^4-6 z^2 a^{-2} +2 z^2 a^{-4} -3 z^2 a^{-6} +2 z^2 a^{-8} +3 z^2- a^{-2} - a^{-4} + a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +12 z^{10} a^{-4} +8 z^{10} a^{-6} +3 z^9 a^{-1} +4 z^9 a^{-3} +15 z^9 a^{-5} +14 z^9 a^{-7} -13 z^8 a^{-2} -37 z^8 a^{-4} -7 z^8 a^{-6} +16 z^8 a^{-8} +z^8-13 z^7 a^{-1} -38 z^7 a^{-3} -65 z^7 a^{-5} -26 z^7 a^{-7} +14 z^7 a^{-9} +6 z^6 a^{-2} +26 z^6 a^{-4} -20 z^6 a^{-6} -26 z^6 a^{-8} +9 z^6 a^{-10} -5 z^6+18 z^5 a^{-1} +54 z^5 a^{-3} +71 z^5 a^{-5} +13 z^5 a^{-7} -18 z^5 a^{-9} +4 z^5 a^{-11} +11 z^4 a^{-2} -z^4 a^{-4} +16 z^4 a^{-6} +11 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +9 z^4-9 z^3 a^{-1} -23 z^3 a^{-3} -31 z^3 a^{-5} -9 z^3 a^{-7} +7 z^3 a^{-9} -z^3 a^{-11} -8 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} -7 z^2+z a^{-1} +3 z a^{-3} +5 z a^{-5} +3 z a^{-7} + a^{-2} - a^{-4} - a^{-6} +2 }[/math] |
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