K12a1153
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+7 q^8-12 q^7+16 q^6-20 q^5+21 q^4-19 q^3+16 q^2-11 q+7-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+20 t^2-26 t+27-26 t^{-1} +20 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-8 z^4-2 z^2+1 }[/math] |
| Determinant | 137 |
| 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} +4 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-4 z^2 a^{-2} +z^2 a^{-4} -5 z^2 a^{-6} +3 z^2 a^{-8} +3 z^2+ a^{-2} - a^{-4} - a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +10 z^{10} a^{-4} +6 z^{10} a^{-6} +3 z^9 a^{-1} +6 z^9 a^{-5} +9 z^9 a^{-7} -16 z^8 a^{-2} -37 z^8 a^{-4} -10 z^8 a^{-6} +10 z^8 a^{-8} +z^8-14 z^7 a^{-1} -25 z^7 a^{-3} -38 z^7 a^{-5} -18 z^7 a^{-7} +9 z^7 a^{-9} +16 z^6 a^{-2} +40 z^6 a^{-4} -5 z^6 a^{-6} -18 z^6 a^{-8} +6 z^6 a^{-10} -5 z^6+20 z^5 a^{-1} +40 z^5 a^{-3} +46 z^5 a^{-5} +9 z^5 a^{-7} -14 z^5 a^{-9} +3 z^5 a^{-11} -2 z^4 a^{-2} -19 z^4 a^{-4} +10 z^4 a^{-6} +12 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +8 z^4-10 z^3 a^{-1} -19 z^3 a^{-3} -23 z^3 a^{-5} -z^3 a^{-7} +11 z^3 a^{-9} -2 z^3 a^{-11} +7 z^2 a^{-4} -6 z^2 a^{-6} -4 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-12} -5 z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} -2 z a^{-7} -3 z a^{-9} - a^{-2} - a^{-4} + a^{-6} + a^{-8} +1 }[/math] |
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