K12a953
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+7 q^{10}-14 q^9+21 q^8-27 q^7+29 q^6-28 q^5+24 q^4-16 q^3+10 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-42 t+53-42 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -4 z^4 a^{-6} -2 z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +4 z^2 a^{-4} -2 z^2 a^{-6} -3 z^2 a^{-8} +2 z^2 a^{-10} +3 a^{-4} - a^{-6} -2 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +12 z^{10} a^{-8} +6 z^{10} a^{-10} +9 z^9 a^{-5} +12 z^9 a^{-7} +10 z^9 a^{-9} +7 z^9 a^{-11} +8 z^8 a^{-4} -2 z^8 a^{-6} -28 z^8 a^{-8} -13 z^8 a^{-10} +5 z^8 a^{-12} +4 z^7 a^{-3} -17 z^7 a^{-5} -41 z^7 a^{-7} -42 z^7 a^{-9} -19 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -18 z^6 a^{-4} -19 z^6 a^{-6} +29 z^6 a^{-8} +17 z^6 a^{-10} -11 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +8 z^5 a^{-5} +52 z^5 a^{-7} +71 z^5 a^{-9} +27 z^5 a^{-11} -8 z^5 a^{-13} -2 z^4 a^{-2} +13 z^4 a^{-4} +23 z^4 a^{-6} -11 z^4 a^{-8} -10 z^4 a^{-10} +6 z^4 a^{-12} -3 z^4 a^{-14} +3 z^3 a^{-3} -3 z^3 a^{-5} -31 z^3 a^{-7} -52 z^3 a^{-9} -22 z^3 a^{-11} +5 z^3 a^{-13} +z^2 a^{-2} -8 z^2 a^{-4} -9 z^2 a^{-6} +4 z^2 a^{-8} +z^2 a^{-10} -z^2 a^{-12} +2 z^2 a^{-14} +8 z a^{-7} +14 z a^{-9} +6 z a^{-11} +3 a^{-4} + a^{-6} -2 a^{-8} - a^{-10} }[/math] |
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