K12n418
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+q^{10}-q^8+2 q^7-3 q^6+4 q^5-4 q^4+4 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-4 t^2+t+1+ t^{-1} -4 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6+5 z^2+1 }[/math] |
| Determinant | 19 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +z^6 a^{-8} +5 z^4 a^{-4} -11 z^4 a^{-6} +6 z^4 a^{-8} +7 z^2 a^{-4} -9 z^2 a^{-6} +9 z^2 a^{-8} -2 z^2 a^{-10} +3 a^{-4} -4 a^{-6} +4 a^{-8} -2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +4 z^9 a^{-7} +2 z^9 a^{-9} +z^8 a^{-4} -2 z^8 a^{-6} -2 z^8 a^{-8} +z^8 a^{-10} -11 z^7 a^{-5} -22 z^7 a^{-7} -11 z^7 a^{-9} -6 z^6 a^{-4} -12 z^6 a^{-6} -14 z^6 a^{-8} -7 z^6 a^{-10} +z^6 a^{-12} +17 z^5 a^{-5} +31 z^5 a^{-7} +12 z^5 a^{-9} -z^5 a^{-11} +z^5 a^{-13} +12 z^4 a^{-4} +30 z^4 a^{-6} +33 z^4 a^{-8} +10 z^4 a^{-10} -5 z^4 a^{-12} -8 z^3 a^{-5} -12 z^3 a^{-7} -z^3 a^{-9} -z^3 a^{-11} -4 z^3 a^{-13} -10 z^2 a^{-4} -20 z^2 a^{-6} -20 z^2 a^{-8} -7 z^2 a^{-10} +3 z^2 a^{-12} +z a^{-7} -z a^{-9} +2 z a^{-13} +3 a^{-4} +4 a^{-6} +4 a^{-8} +2 a^{-10} }[/math] |
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