K12a841
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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+20 q^6-19 q^5+17 q^4-11 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-28 t+33-28 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4+1 }[/math] |
| Determinant | 129 |
| 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} +4 z^2 a^{-4} -5 z^2 a^{-6} -4 z^2 a^{-8} +3 z^2 a^{-10} +4 a^{-4} -2 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} -15 z^8 a^{-8} -7 z^8 a^{-10} +3 z^8 a^{-12} +3 z^7 a^{-3} -11 z^7 a^{-5} -23 z^7 a^{-7} -25 z^7 a^{-9} -14 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-2} -14 z^6 a^{-4} -19 z^6 a^{-6} +14 z^6 a^{-8} +9 z^6 a^{-10} -8 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +6 z^5 a^{-5} +32 z^5 a^{-7} +52 z^5 a^{-9} +28 z^5 a^{-11} -6 z^5 a^{-13} -3 z^4 a^{-2} +14 z^4 a^{-4} +33 z^4 a^{-6} +3 z^4 a^{-8} -2 z^4 a^{-10} +7 z^4 a^{-12} -4 z^4 a^{-14} +4 z^3 a^{-3} -z^3 a^{-5} -17 z^3 a^{-7} -47 z^3 a^{-9} -31 z^3 a^{-11} +4 z^3 a^{-13} +2 z^2 a^{-2} -12 z^2 a^{-4} -19 z^2 a^{-6} -3 z^2 a^{-10} -4 z^2 a^{-12} +4 z^2 a^{-14} -2 z a^{-5} +6 z a^{-7} +18 z a^{-9} +10 z a^{-11} +4 a^{-4} +2 a^{-6} -3 a^{-8} -2 a^{-10} }[/math] |
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