K12a266
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-11 q^9+19 q^8-28 q^7+33 q^6-35 q^5+32 q^4-25 q^3+18 q^2-9 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+28 t^2-44 t+51-44 t^{-1} +28 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +3 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +7 z^4 a^{-4} -2 z^4 a^{-8} -2 z^2 a^{-2} +9 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +5 a^{-4} -6 a^{-6} +2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +17 z^{10} a^{-6} +10 z^{10} a^{-8} +7 z^9 a^{-3} +10 z^9 a^{-5} +18 z^9 a^{-7} +15 z^9 a^{-9} +4 z^8 a^{-2} -13 z^8 a^{-4} -37 z^8 a^{-6} -5 z^8 a^{-8} +15 z^8 a^{-10} +z^7 a^{-1} -20 z^7 a^{-3} -46 z^7 a^{-5} -54 z^7 a^{-7} -18 z^7 a^{-9} +11 z^7 a^{-11} -13 z^6 a^{-2} -5 z^6 a^{-4} +16 z^6 a^{-6} -15 z^6 a^{-8} -18 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +16 z^5 a^{-3} +46 z^5 a^{-5} +39 z^5 a^{-7} -2 z^5 a^{-9} -13 z^5 a^{-11} +z^5 a^{-13} +13 z^4 a^{-2} +20 z^4 a^{-4} +13 z^4 a^{-6} +11 z^4 a^{-8} +z^4 a^{-10} -4 z^4 a^{-12} +2 z^3 a^{-1} -5 z^3 a^{-3} -12 z^3 a^{-5} +2 z^3 a^{-7} +10 z^3 a^{-9} +3 z^3 a^{-11} -5 z^2 a^{-2} -16 z^2 a^{-4} -15 z^2 a^{-6} -z^2 a^{-8} +3 z^2 a^{-10} +z a^{-3} -3 z a^{-5} -8 z a^{-7} -4 z a^{-9} +5 a^{-4} +6 a^{-6} +2 a^{-8} }[/math] |
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