K12a592
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+10 q^{10}-19 q^9+27 q^8-33 q^7+35 q^6-32 q^5+26 q^4-17 q^3+9 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+24 t^2-49 t+61-49 t^{-1} +24 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-6 z^4+2 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -8 z^4 a^{-6} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -6 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} + a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +13 z^{10} a^{-8} +7 z^{10} a^{-10} +8 z^9 a^{-5} +16 z^9 a^{-7} +18 z^9 a^{-9} +10 z^9 a^{-11} +6 z^8 a^{-4} +z^8 a^{-6} -13 z^8 a^{-8} +8 z^8 a^{-12} +3 z^7 a^{-3} -13 z^7 a^{-5} -39 z^7 a^{-7} -43 z^7 a^{-9} -16 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -11 z^6 a^{-4} -19 z^6 a^{-6} -9 z^6 a^{-8} -18 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} +10 z^5 a^{-5} +34 z^5 a^{-7} +33 z^5 a^{-9} +7 z^5 a^{-11} -8 z^5 a^{-13} -3 z^4 a^{-2} +8 z^4 a^{-4} +22 z^4 a^{-6} +13 z^4 a^{-8} +13 z^4 a^{-10} +9 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -5 z^3 a^{-5} -15 z^3 a^{-7} -13 z^3 a^{-9} -z^3 a^{-11} +5 z^3 a^{-13} +3 z^2 a^{-2} -4 z^2 a^{-4} -10 z^2 a^{-6} -3 z^2 a^{-8} -3 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +3 z a^{-7} +3 z a^{-9} -z a^{-11} -z a^{-13} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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