K12n581
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^{12}+2 q^{11}-3 q^{10}+5 q^9-4 q^8+4 q^7-3 q^6+2 q^5-q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-5 t^2+4 t-3+4 t^{-1} -5 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+13 z^4+11 z^2+1 }[/math] |
| Determinant | 27 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-6} +4 z^4 a^{-8} +5 z^4 a^{-10} -z^4 a^{-12} +6 z^2 a^{-6} +3 z^2 a^{-8} +7 z^2 a^{-10} -5 z^2 a^{-12} + a^{-6} +4 a^{-10} -5 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +2 z^9 a^{-11} +z^9 a^{-13} +z^8 a^{-8} -7 z^8 a^{-10} -8 z^8 a^{-12} +z^7 a^{-7} -5 z^7 a^{-9} -13 z^7 a^{-11} -7 z^7 a^{-13} +z^6 a^{-6} -4 z^6 a^{-8} +20 z^6 a^{-10} +26 z^6 a^{-12} +z^6 a^{-14} -4 z^5 a^{-7} +9 z^5 a^{-9} +31 z^5 a^{-11} +18 z^5 a^{-13} -5 z^4 a^{-6} +4 z^4 a^{-8} -27 z^4 a^{-10} -39 z^4 a^{-12} -3 z^4 a^{-14} +3 z^3 a^{-7} -7 z^3 a^{-9} -27 z^3 a^{-11} -15 z^3 a^{-13} +2 z^3 a^{-15} +6 z^2 a^{-6} -2 z^2 a^{-8} +17 z^2 a^{-10} +29 z^2 a^{-12} +4 z^2 a^{-14} +7 z a^{-11} +3 z a^{-13} -4 z a^{-15} - a^{-6} -4 a^{-10} -5 a^{-12} - a^{-14} }[/math] |
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