K12a777
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-16 q^7+22 q^6-26 q^5+28 q^4-25 q^3+20 q^2-14 q+8-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+23 t^2-36 t+41-36 t^{-1} +23 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-5 z^4+1 }[/math] |
| Determinant | 177 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +4 z^6 a^{-4} -2 z^6 a^{-6} -7 z^4 a^{-2} +6 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +z^4-7 z^2 a^{-2} +6 z^2 a^{-4} -4 z^2 a^{-6} +2 z^2 a^{-8} +3 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +12 z^{10} a^{-4} +8 z^{10} a^{-6} +3 z^9 a^{-1} +5 z^9 a^{-3} +17 z^9 a^{-5} +15 z^9 a^{-7} -12 z^8 a^{-2} -31 z^8 a^{-4} +18 z^8 a^{-8} +z^8-13 z^7 a^{-1} -40 z^7 a^{-3} -66 z^7 a^{-5} -24 z^7 a^{-7} +15 z^7 a^{-9} +2 z^6 a^{-2} +2 z^6 a^{-4} -46 z^6 a^{-6} -32 z^6 a^{-8} +9 z^6 a^{-10} -5 z^6+19 z^5 a^{-1} +54 z^5 a^{-3} +57 z^5 a^{-5} -2 z^5 a^{-7} -20 z^5 a^{-9} +4 z^5 a^{-11} +19 z^4 a^{-2} +33 z^4 a^{-4} +48 z^4 a^{-6} +18 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +9 z^4-11 z^3 a^{-1} -22 z^3 a^{-3} -11 z^3 a^{-5} +10 z^3 a^{-7} +9 z^3 a^{-9} -z^3 a^{-11} -16 z^2 a^{-2} -19 z^2 a^{-4} -16 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -7 z^2+2 z a^{-1} +3 z a^{-3} -z a^{-5} -3 z a^{-7} -z a^{-9} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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