K12a1186
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+4 q^{10}-10 q^9+19 q^8-29 q^7+36 q^6-39 q^5+37 q^4-30 q^3+22 q^2-12 q+5- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+30 t^2-50 t+59-50 t^{-1} +30 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 245 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +3 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -2 z^4 a^{-2} +2 z^4 a^{-4} +7 z^4 a^{-6} -3 z^4 a^{-8} +6 z^2 a^{-6} -3 z^2 a^{-8} + a^{-2} + a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +10 z^{10} a^{-4} +22 z^{10} a^{-6} +12 z^{10} a^{-8} +10 z^9 a^{-3} +14 z^9 a^{-5} +20 z^9 a^{-7} +16 z^9 a^{-9} +5 z^8 a^{-2} -18 z^8 a^{-4} -48 z^8 a^{-6} -11 z^8 a^{-8} +14 z^8 a^{-10} +z^7 a^{-1} -26 z^7 a^{-3} -58 z^7 a^{-5} -65 z^7 a^{-7} -25 z^7 a^{-9} +9 z^7 a^{-11} -13 z^6 a^{-2} -2 z^6 a^{-4} +29 z^6 a^{-6} -6 z^6 a^{-8} -20 z^6 a^{-10} +4 z^6 a^{-12} -2 z^5 a^{-1} +18 z^5 a^{-3} +50 z^5 a^{-5} +59 z^5 a^{-7} +17 z^5 a^{-9} -11 z^5 a^{-11} +z^5 a^{-13} +10 z^4 a^{-2} +7 z^4 a^{-4} -14 z^4 a^{-6} +6 z^4 a^{-8} +13 z^4 a^{-10} -4 z^4 a^{-12} +z^3 a^{-1} -3 z^3 a^{-3} -17 z^3 a^{-5} -24 z^3 a^{-7} -4 z^3 a^{-9} +6 z^3 a^{-11} -z^3 a^{-13} -z^2 a^{-2} +z^2 a^{-4} +7 z^2 a^{-6} +2 z^2 a^{-8} -2 z^2 a^{-10} +z^2 a^{-12} +z a^{-3} +2 z a^{-5} +3 z a^{-7} +z a^{-9} -z a^{-11} - a^{-2} - a^{-6} - a^{-8} }[/math] |
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