K12a253
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+8 q^{10}-14 q^9+20 q^8-24 q^7+25 q^6-23 q^5+19 q^4-12 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+19 t^2-36 t+43-36 t^{-1} +19 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-5 z^4+4 z^2+1 }[/math] |
| Determinant | 161 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -5 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} +3 a^{-4} -3 a^{-6} +2 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +5 z^9 a^{-5} +9 z^9 a^{-7} +11 z^9 a^{-9} +7 z^9 a^{-11} +5 z^8 a^{-4} +3 z^8 a^{-6} -8 z^8 a^{-8} +z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -9 z^7 a^{-5} -25 z^7 a^{-7} -31 z^7 a^{-9} -14 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -13 z^6 a^{-4} -20 z^6 a^{-6} -6 z^6 a^{-8} -19 z^6 a^{-10} -18 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +6 z^5 a^{-5} +32 z^5 a^{-7} +34 z^5 a^{-9} +6 z^5 a^{-11} -10 z^5 a^{-13} -3 z^4 a^{-2} +13 z^4 a^{-4} +29 z^4 a^{-6} +21 z^4 a^{-8} +23 z^4 a^{-10} +13 z^4 a^{-12} -2 z^4 a^{-14} +5 z^3 a^{-3} -4 z^3 a^{-5} -21 z^3 a^{-7} -16 z^3 a^{-9} +z^3 a^{-11} +5 z^3 a^{-13} +2 z^2 a^{-2} -9 z^2 a^{-4} -18 z^2 a^{-6} -13 z^2 a^{-8} -9 z^2 a^{-10} -3 z^2 a^{-12} +z a^{-5} +5 z a^{-7} +3 z a^{-9} -z a^{-11} +3 a^{-4} +3 a^{-6} +2 a^{-8} + a^{-10} }[/math] |
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