K12a205
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+8 q^{11}-13 q^{10}+18 q^9-21 q^8+21 q^7-19 q^6+15 q^5-10 q^4+6 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-18 t^2+26 t-29+26 t^{-1} -18 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-4 z^4+3 z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -9 z^4 a^{-6} -3 z^4 a^{-8} +3 z^4 a^{-10} +8 z^2 a^{-4} -9 z^2 a^{-6} +3 z^2 a^{-8} +z^2 a^{-10} +4 a^{-4} -5 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +6 z^{10} a^{-8} +4 z^{10} a^{-10} +2 z^9 a^{-5} +3 z^9 a^{-7} +9 z^9 a^{-9} +8 z^9 a^{-11} +z^8 a^{-4} -4 z^8 a^{-6} -12 z^8 a^{-8} +4 z^8 a^{-10} +11 z^8 a^{-12} -9 z^7 a^{-5} -19 z^7 a^{-7} -26 z^7 a^{-9} -5 z^7 a^{-11} +11 z^7 a^{-13} -6 z^6 a^{-4} -10 z^6 a^{-6} -10 z^6 a^{-8} -27 z^6 a^{-10} -13 z^6 a^{-12} +8 z^6 a^{-14} +12 z^5 a^{-5} +17 z^5 a^{-7} +4 z^5 a^{-9} -18 z^5 a^{-11} -13 z^5 a^{-13} +4 z^5 a^{-15} +13 z^4 a^{-4} +29 z^4 a^{-6} +26 z^4 a^{-8} +17 z^4 a^{-10} -z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -3 z^3 a^{-5} +3 z^3 a^{-7} +16 z^3 a^{-9} +17 z^3 a^{-11} +5 z^3 a^{-13} -2 z^3 a^{-15} -12 z^2 a^{-4} -21 z^2 a^{-6} -13 z^2 a^{-8} -3 z^2 a^{-10} +3 z^2 a^{-12} +2 z^2 a^{-14} -2 z a^{-5} -4 z a^{-7} -6 z a^{-9} -5 z a^{-11} -z a^{-13} +4 a^{-4} +5 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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