K12a154
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+10 q^{10}-20 q^9+29 q^8-36 q^7+39 q^6-36 q^5+30 q^4-20 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+24 t^2-56 t+73-56 t^{-1} +24 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6+4 z^2+1 }[/math] |
| Determinant | 241 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} +z^4 a^{-2} +z^4 a^{-4} -8 z^4 a^{-6} +6 z^4 a^{-8} +z^2 a^{-2} +5 z^2 a^{-4} -9 z^2 a^{-6} +11 z^2 a^{-8} -4 z^2 a^{-10} +3 a^{-4} -4 a^{-6} +5 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +8 z^{10} a^{-6} +15 z^{10} a^{-8} +7 z^{10} a^{-10} +12 z^9 a^{-5} +26 z^9 a^{-7} +24 z^9 a^{-9} +10 z^9 a^{-11} +9 z^8 a^{-4} +4 z^8 a^{-6} -6 z^8 a^{-8} +7 z^8 a^{-10} +8 z^8 a^{-12} +4 z^7 a^{-3} -22 z^7 a^{-5} -66 z^7 a^{-7} -56 z^7 a^{-9} -12 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -18 z^6 a^{-4} -39 z^6 a^{-6} -43 z^6 a^{-8} -38 z^6 a^{-10} -14 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +17 z^5 a^{-5} +58 z^5 a^{-7} +40 z^5 a^{-9} -2 z^5 a^{-11} -8 z^5 a^{-13} -2 z^4 a^{-2} +16 z^4 a^{-4} +47 z^4 a^{-6} +56 z^4 a^{-8} +38 z^4 a^{-10} +9 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -8 z^3 a^{-5} -25 z^3 a^{-7} -11 z^3 a^{-9} +9 z^3 a^{-11} +6 z^3 a^{-13} +z^2 a^{-2} -10 z^2 a^{-4} -24 z^2 a^{-6} -27 z^2 a^{-8} -18 z^2 a^{-10} -3 z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +5 z a^{-7} +z a^{-9} -5 z a^{-11} -2 z a^{-13} +3 a^{-4} +4 a^{-6} +5 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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