K12a685
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+10 q^{10}-18 q^9+25 q^8-31 q^7+32 q^6-29 q^5+24 q^4-15 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+21 t^2-46 t+59-46 t^{-1} +21 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -3 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} + a^{-2} +2 a^{-6} -3 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +5 z^{10} a^{-6} +12 z^{10} a^{-8} +7 z^{10} a^{-10} +6 z^9 a^{-5} +10 z^9 a^{-7} +14 z^9 a^{-9} +10 z^9 a^{-11} +5 z^8 a^{-4} -z^8 a^{-6} -20 z^8 a^{-8} -6 z^8 a^{-10} +8 z^8 a^{-12} +3 z^7 a^{-3} -6 z^7 a^{-5} -22 z^7 a^{-7} -37 z^7 a^{-9} -20 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -8 z^6 a^{-4} -6 z^6 a^{-6} +19 z^6 a^{-8} -z^6 a^{-10} -16 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} -4 z^5 a^{-5} +17 z^5 a^{-7} +39 z^5 a^{-9} +17 z^5 a^{-11} -8 z^5 a^{-13} -3 z^4 a^{-2} +2 z^4 a^{-4} +2 z^4 a^{-6} -18 z^4 a^{-8} -4 z^4 a^{-10} +9 z^4 a^{-12} -2 z^4 a^{-14} +5 z^3 a^{-3} +8 z^3 a^{-5} -8 z^3 a^{-7} -27 z^3 a^{-9} -12 z^3 a^{-11} +4 z^3 a^{-13} +3 z^2 a^{-2} +z^2 a^{-4} +3 z^2 a^{-6} +10 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -z a^{-3} -3 z a^{-5} +3 z a^{-7} +9 z a^{-9} +4 z a^{-11} - a^{-2} -2 a^{-6} -3 a^{-8} - a^{-10} }[/math] |
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