K12a239
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-3 q^{10}+5 q^9-7 q^8+10 q^7-12 q^6+12 q^5-12 q^4+10 q^3-7 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+22 t-31+22 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-2 z^2+1 }[/math] |
| Determinant | 87 |
| 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} -2 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-10} +z^2+ a^{-2} - a^{-4} - a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +3 z^9 a^{-5} +z^9 a^{-7} +z^9 a^{-9} +3 z^9 a^{-11} +3 z^8 a^{-4} -2 z^8 a^{-6} -20 z^8 a^{-8} -14 z^8 a^{-10} +z^8 a^{-12} +3 z^7 a^{-3} -6 z^7 a^{-5} -13 z^7 a^{-7} -20 z^7 a^{-9} -16 z^7 a^{-11} +3 z^6 a^{-2} -2 z^6 a^{-4} -7 z^6 a^{-6} +20 z^6 a^{-8} +17 z^6 a^{-10} -5 z^6 a^{-12} +2 z^5 a^{-1} -z^5 a^{-3} +8 z^5 a^{-5} +17 z^5 a^{-7} +31 z^5 a^{-9} +25 z^5 a^{-11} -3 z^4 a^{-2} -2 z^4 a^{-4} +11 z^4 a^{-6} -2 z^4 a^{-8} -4 z^4 a^{-10} +7 z^4 a^{-12} +z^4-2 z^3 a^{-1} -2 z^3 a^{-3} -11 z^3 a^{-5} -11 z^3 a^{-7} -12 z^3 a^{-9} -12 z^3 a^{-11} +2 z^2 a^{-2} +3 z^2 a^{-4} -8 z^2 a^{-6} -5 z^2 a^{-8} -z^2 a^{-10} -3 z^2 a^{-12} -2 z^2+2 z a^{-3} +5 z a^{-5} +3 z a^{-7} +z a^{-9} +z a^{-11} - a^{-2} - a^{-4} + a^{-6} + a^{-8} +1 }[/math] |
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