K12a270
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-3 q^{10}+5 q^9-9 q^8+12 q^7-13 q^6+15 q^5-14 q^4+11 q^3-8 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+25 t-37+25 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4+z^2+1 }[/math] |
| Determinant | 99 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -2 z^4 a^{-4} -2 z^4 a^{-6} -z^4 a^{-8} -z^2 a^{-4} +z^2 a^{-10} +z^2- a^{-4} +2 a^{-6} - a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +4 z^9 a^{-5} +4 z^9 a^{-7} +3 z^9 a^{-9} +3 z^9 a^{-11} +4 z^8 a^{-4} -6 z^8 a^{-6} -24 z^8 a^{-8} -13 z^8 a^{-10} +z^8 a^{-12} +4 z^7 a^{-3} -7 z^7 a^{-5} -25 z^7 a^{-7} -30 z^7 a^{-9} -16 z^7 a^{-11} +3 z^6 a^{-2} -4 z^6 a^{-4} +4 z^6 a^{-6} +31 z^6 a^{-8} +15 z^6 a^{-10} -5 z^6 a^{-12} +2 z^5 a^{-1} -5 z^5 a^{-3} +2 z^5 a^{-5} +35 z^5 a^{-7} +53 z^5 a^{-9} +27 z^5 a^{-11} -2 z^4 a^{-2} -2 z^4 a^{-4} -11 z^4 a^{-6} -24 z^4 a^{-8} -5 z^4 a^{-10} +7 z^4 a^{-12} +z^4-2 z^3 a^{-1} +5 z^3 a^{-3} +2 z^3 a^{-5} -24 z^3 a^{-7} -35 z^3 a^{-9} -16 z^3 a^{-11} +5 z^2 a^{-4} +11 z^2 a^{-6} +12 z^2 a^{-8} +2 z^2 a^{-10} -2 z^2 a^{-12} -2 z^2-2 z a^{-3} -2 z a^{-5} +5 z a^{-7} +7 z a^{-9} +2 z a^{-11} - a^{-4} -2 a^{-6} - a^{-8} +1 }[/math] |
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