K12n526
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-q^8-q^7+2 q^6-4 q^5+5 q^4-5 q^3+6 q^2-4 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+6 t^2-3 t+1-3 t^{-1} +6 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 29 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +12 z^4 a^{-4} -6 z^4 a^{-6} -3 z^2 a^{-2} +12 z^2 a^{-4} -10 z^2 a^{-6} +2 z^2 a^{-8} +5 a^{-4} -6 a^{-6} +2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +4 z^9 a^{-5} +z^9 a^{-7} +3 z^8 a^{-2} -3 z^8 a^{-6} +z^7 a^{-1} -13 z^7 a^{-3} -20 z^7 a^{-5} -5 z^7 a^{-7} +z^7 a^{-9} -14 z^6 a^{-2} -19 z^6 a^{-4} -7 z^6 a^{-6} -z^6 a^{-8} +z^6 a^{-10} -4 z^5 a^{-1} +12 z^5 a^{-3} +24 z^5 a^{-5} +z^5 a^{-7} -7 z^5 a^{-9} +17 z^4 a^{-2} +34 z^4 a^{-4} +22 z^4 a^{-6} -5 z^4 a^{-10} +3 z^3 a^{-1} -3 z^3 a^{-3} -5 z^3 a^{-5} +11 z^3 a^{-7} +10 z^3 a^{-9} -7 z^2 a^{-2} -21 z^2 a^{-4} -18 z^2 a^{-6} +4 z^2 a^{-10} +z a^{-3} -3 z a^{-5} -8 z a^{-7} -4 z a^{-9} +5 a^{-4} +6 a^{-6} +2 a^{-8} }[/math] |
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