K12a522
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-15 q^9+21 q^8-26 q^7+27 q^6-25 q^5+20 q^4-13 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+19 t^2-39 t+49-39 t^{-1} +19 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-5 z^4+z^2+1 }[/math] |
| Determinant | 173 |
| 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} -5 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +2 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} + a^{-2} +2 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +5 z^9 a^{-5} +10 z^9 a^{-7} +12 z^9 a^{-9} +7 z^9 a^{-11} +5 z^8 a^{-4} +6 z^8 a^{-6} -2 z^8 a^{-8} +4 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -5 z^7 a^{-5} -19 z^7 a^{-7} -25 z^7 a^{-9} -10 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -10 z^6 a^{-4} -24 z^6 a^{-6} -19 z^6 a^{-8} -22 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} -4 z^5 a^{-5} +7 z^5 a^{-7} +11 z^5 a^{-9} -2 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} +6 z^4 a^{-4} +26 z^4 a^{-6} +25 z^4 a^{-8} +18 z^4 a^{-10} +8 z^4 a^{-12} -2 z^4 a^{-14} +4 z^3 a^{-3} +5 z^3 a^{-5} +8 z^3 a^{-7} +7 z^3 a^{-9} +5 z^3 a^{-11} +5 z^3 a^{-13} +3 z^2 a^{-2} -4 z^2 a^{-4} -14 z^2 a^{-6} -8 z^2 a^{-8} -4 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} -3 z a^{-5} -5 z a^{-7} -3 z a^{-9} -2 z a^{-11} -z a^{-13} - a^{-2} +2 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
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