K12a521
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+6 q^8-10 q^7+13 q^6-16 q^5+17 q^4-15 q^3+13 q^2-9 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+17 t^2-21 t+21-21 t^{-1} +17 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-5 z^4+1 }[/math] |
| Determinant | 113 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -8 z^4 a^{-2} +9 z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-8} +z^4-7 z^2 a^{-2} +9 z^2 a^{-4} -8 z^2 a^{-6} +3 z^2 a^{-8} +3 z^2- a^{-2} +3 a^{-4} -3 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +3 z^9 a^{-1} +4 z^9 a^{-3} +6 z^9 a^{-5} +5 z^9 a^{-7} -11 z^8 a^{-2} -18 z^8 a^{-4} +6 z^8 a^{-8} +z^8-15 z^7 a^{-1} -31 z^7 a^{-3} -28 z^7 a^{-5} -6 z^7 a^{-7} +6 z^7 a^{-9} +5 z^6 a^{-2} +4 z^6 a^{-4} -18 z^6 a^{-6} -7 z^6 a^{-8} +5 z^6 a^{-10} -5 z^6+23 z^5 a^{-1} +44 z^5 a^{-3} +27 z^5 a^{-5} -3 z^5 a^{-7} -6 z^5 a^{-9} +3 z^5 a^{-11} +12 z^4 a^{-2} +17 z^4 a^{-4} +21 z^4 a^{-6} +2 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +8 z^4-12 z^3 a^{-1} -18 z^3 a^{-3} -7 z^3 a^{-5} +4 z^3 a^{-7} +2 z^3 a^{-9} -3 z^3 a^{-11} -9 z^2 a^{-2} -11 z^2 a^{-4} -12 z^2 a^{-6} -2 z^2 a^{-8} +2 z^2 a^{-10} -z^2 a^{-12} -5 z^2+z a^{-1} +2 z a^{-3} -z a^{-5} -3 z a^{-7} +z a^{-11} + a^{-2} +3 a^{-4} +3 a^{-6} + a^{-8} +1 }[/math] |
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