K12n887
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-10 q^9+15 q^8-20 q^7+21 q^6-20 q^5+16 q^4-10 q^3+6 q^2-q }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+16 t^2-25 t+29-25 t^{-1} +16 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6+z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-6} -z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -z^4 a^{-4} +3 z^4 a^{-6} -2 z^4 a^{-8} +5 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +5 a^{-4} -6 a^{-6} +2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +z^9 a^{-5} +6 z^9 a^{-7} +5 z^9 a^{-9} +5 z^8 a^{-6} +15 z^8 a^{-8} +10 z^8 a^{-10} +6 z^7 a^{-5} +6 z^7 a^{-7} +10 z^7 a^{-9} +10 z^7 a^{-11} +6 z^6 a^{-4} -3 z^6 a^{-6} -24 z^6 a^{-8} -10 z^6 a^{-10} +5 z^6 a^{-12} +z^5 a^{-3} -12 z^5 a^{-5} -32 z^5 a^{-7} -35 z^5 a^{-9} -15 z^5 a^{-11} +z^5 a^{-13} -6 z^4 a^{-4} -3 z^4 a^{-6} +3 z^4 a^{-8} -5 z^4 a^{-10} -5 z^4 a^{-12} +10 z^3 a^{-5} +30 z^3 a^{-7} +25 z^3 a^{-9} +5 z^3 a^{-11} -5 z^2 a^{-4} -6 z^2 a^{-6} +4 z^2 a^{-8} +5 z^2 a^{-10} -6 z a^{-5} -11 z a^{-7} -5 z a^{-9} +5 a^{-4} +6 a^{-6} +2 a^{-8} }[/math] |
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