K12a780
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+11 q^{10}-20 q^9+28 q^8-35 q^7+36 q^6-33 q^5+27 q^4-17 q^3+9 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+24 t^2-51 t+65-51 t^{-1} +24 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-6 z^4+1 }[/math] |
| Determinant | 225 |
| 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} -7 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} + a^{-2} +2 a^{-4} -2 a^{-6} - a^{-8} + a^{-10} }[/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} +17 z^9 a^{-7} +20 z^9 a^{-9} +11 z^9 a^{-11} +6 z^8 a^{-4} +3 z^8 a^{-6} -6 z^8 a^{-8} +6 z^8 a^{-10} +9 z^8 a^{-12} +3 z^7 a^{-3} -12 z^7 a^{-5} -36 z^7 a^{-7} -42 z^7 a^{-9} -17 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -11 z^6 a^{-4} -25 z^6 a^{-6} -30 z^6 a^{-8} -36 z^6 a^{-10} -18 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} +7 z^5 a^{-5} +17 z^5 a^{-7} +18 z^5 a^{-9} +7 z^5 a^{-11} -7 z^5 a^{-13} -3 z^4 a^{-2} +9 z^4 a^{-4} +31 z^4 a^{-6} +32 z^4 a^{-8} +30 z^4 a^{-10} +15 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} +z^3 a^{-5} +7 z^3 a^{-7} +2 z^3 a^{-9} -3 z^3 a^{-11} +4 z^3 a^{-13} +3 z^2 a^{-2} -6 z^2 a^{-4} -16 z^2 a^{-6} -7 z^2 a^{-8} -8 z^2 a^{-10} -7 z^2 a^{-12} +z^2 a^{-14} -4 z a^{-5} -5 z a^{-7} +z a^{-9} +z a^{-11} -z a^{-13} - a^{-2} +2 a^{-4} +2 a^{-6} - a^{-8} - a^{-10} }[/math] |
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