K12a538
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+5 q^{11}-8 q^{10}+10 q^9-12 q^8+12 q^7-10 q^6+9 q^5-6 q^4+4 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-12 t^2+13 t-13+13 t^{-1} -12 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-4 z^4+5 z^2+1 }[/math] |
| Determinant | 83 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -6 z^4 a^{-6} -7 z^4 a^{-8} +4 z^4 a^{-10} +6 z^2 a^{-4} -4 z^2 a^{-8} +3 z^2 a^{-10} + a^{-4} +2 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} -z^9 a^{-7} +z^9 a^{-9} +4 z^9 a^{-11} +z^8 a^{-4} -9 z^8 a^{-6} -24 z^8 a^{-8} -10 z^8 a^{-10} +4 z^8 a^{-12} -11 z^7 a^{-5} -12 z^7 a^{-7} -16 z^7 a^{-9} -11 z^7 a^{-11} +4 z^7 a^{-13} -6 z^6 a^{-4} +10 z^6 a^{-6} +39 z^6 a^{-8} +13 z^6 a^{-10} -6 z^6 a^{-12} +4 z^6 a^{-14} +18 z^5 a^{-5} +25 z^5 a^{-7} +25 z^5 a^{-9} +12 z^5 a^{-11} -3 z^5 a^{-13} +3 z^5 a^{-15} +11 z^4 a^{-4} -4 z^4 a^{-6} -33 z^4 a^{-8} -10 z^4 a^{-10} +3 z^4 a^{-12} -4 z^4 a^{-14} +z^4 a^{-16} -10 z^3 a^{-5} -18 z^3 a^{-7} -14 z^3 a^{-9} -4 z^3 a^{-11} -2 z^3 a^{-13} -4 z^3 a^{-15} -7 z^2 a^{-4} +4 z^2 a^{-6} +15 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-16} +z a^{-5} +5 z a^{-7} +2 z a^{-9} -z a^{-11} +2 z a^{-13} +z a^{-15} + a^{-4} -2 a^{-6} -2 a^{-8} }[/math] |
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