K12a252
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+8 q^{11}-13 q^{10}+17 q^9-20 q^8+20 q^7-17 q^6+14 q^5-9 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-17 t^2+24 t-27+24 t^{-1} -17 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-3 z^4+5 z^2+1 }[/math] |
| Determinant | 131 |
| 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} -8 z^4 a^{-6} -3 z^4 a^{-8} +3 z^4 a^{-10} +7 z^2 a^{-4} -5 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} +2 a^{-4} - a^{-6} + 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} +2 z^9 a^{-7} +8 z^9 a^{-9} +8 z^9 a^{-11} +z^8 a^{-4} -6 z^8 a^{-6} -17 z^8 a^{-8} +z^8 a^{-10} +11 z^8 a^{-12} -10 z^7 a^{-5} -19 z^7 a^{-7} -29 z^7 a^{-9} -9 z^7 a^{-11} +11 z^7 a^{-13} -6 z^6 a^{-4} -z^6 a^{-6} +8 z^6 a^{-8} -21 z^6 a^{-10} -16 z^6 a^{-12} +8 z^6 a^{-14} +16 z^5 a^{-5} +28 z^5 a^{-7} +22 z^5 a^{-9} -8 z^5 a^{-11} -14 z^5 a^{-13} +4 z^5 a^{-15} +12 z^4 a^{-4} +13 z^4 a^{-6} +5 z^4 a^{-8} +17 z^4 a^{-10} +5 z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -9 z^3 a^{-5} -16 z^3 a^{-7} -4 z^3 a^{-9} +10 z^3 a^{-11} +5 z^3 a^{-13} -2 z^3 a^{-15} -9 z^2 a^{-4} -8 z^2 a^{-6} -3 z^2 a^{-8} -5 z^2 a^{-10} +z^2 a^{-14} +z a^{-5} +4 z a^{-7} -3 z a^{-11} +2 a^{-4} + a^{-6} + a^{-8} + a^{-10} }[/math] |
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