K12a938
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-2 q^{11}+5 q^{10}-10 q^9+14 q^8-19 q^7+21 q^6-20 q^5+17 q^4-12 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-29 t+35-29 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4-z^2+1 }[/math] |
| Determinant | 133 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -6 z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -5 z^2 a^{-6} -4 z^2 a^{-8} +3 z^2 a^{-10} + a^{-2} +2 a^{-4} - a^{-6} -3 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +5 z^9 a^{-5} +6 z^9 a^{-7} +5 z^9 a^{-9} +4 z^9 a^{-11} +5 z^8 a^{-4} +z^8 a^{-6} -14 z^8 a^{-8} -7 z^8 a^{-10} +3 z^8 a^{-12} +3 z^7 a^{-3} -8 z^7 a^{-5} -18 z^7 a^{-7} -23 z^7 a^{-9} -14 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-2} -11 z^6 a^{-4} -17 z^6 a^{-6} +14 z^6 a^{-8} +10 z^6 a^{-10} -8 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} -2 z^5 a^{-5} +15 z^5 a^{-7} +44 z^5 a^{-9} +28 z^5 a^{-11} -6 z^5 a^{-13} -3 z^4 a^{-2} +6 z^4 a^{-4} +21 z^4 a^{-6} -4 z^4 a^{-8} -5 z^4 a^{-10} +7 z^4 a^{-12} -4 z^4 a^{-14} +3 z^3 a^{-3} +5 z^3 a^{-5} +2 z^3 a^{-7} -34 z^3 a^{-9} -30 z^3 a^{-11} +4 z^3 a^{-13} +3 z^2 a^{-2} -6 z^2 a^{-4} -9 z^2 a^{-6} +8 z^2 a^{-8} -4 z^2 a^{-12} +4 z^2 a^{-14} -4 z a^{-5} -z a^{-7} +11 z a^{-9} +8 z a^{-11} - a^{-2} +2 a^{-4} + a^{-6} -3 a^{-8} -2 a^{-10} }[/math] |
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