K12a1161
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+4 q^7-6 q^6+8 q^5-11 q^4+11 q^3-10 q^2+9 q-6+4 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+19 t-25+19 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-5 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^4 a^{-2} -2 z^4 a^{-4} -z^4 a^{-6} -z^4+a^2 z^2-2 z^2 a^{-2} -3 z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} -z^2+a^2+ a^{-2} -2 a^{-4} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +2 z^9 a^{-1} -3 z^9 a^{-3} -2 z^9 a^{-5} +3 z^9 a^{-7} -9 z^8 a^{-2} -21 z^8 a^{-4} -7 z^8 a^{-6} +3 z^8 a^{-8} +2 z^8+2 a z^7-6 z^7 a^{-1} +2 z^7 a^{-3} -5 z^7 a^{-5} -13 z^7 a^{-7} +2 z^7 a^{-9} +a^2 z^6+19 z^6 a^{-2} +44 z^6 a^{-4} +6 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -5 z^6-7 a z^5+6 z^5 a^{-1} +6 z^5 a^{-3} +21 z^5 a^{-5} +21 z^5 a^{-7} -7 z^5 a^{-9} -4 a^2 z^4-18 z^4 a^{-2} -36 z^4 a^{-4} +4 z^4 a^{-6} +14 z^4 a^{-8} -4 z^4 a^{-10} +5 a z^3-4 z^3 a^{-1} -5 z^3 a^{-3} -18 z^3 a^{-5} -18 z^3 a^{-7} +4 z^3 a^{-9} +4 a^2 z^2+5 z^2 a^{-2} +14 z^2 a^{-4} -4 z^2 a^{-6} -8 z^2 a^{-8} +3 z^2 a^{-10} +2 z^2+z a^{-3} +7 z a^{-5} +6 z a^{-7} -a^2- a^{-2} -2 a^{-4} + a^{-8} }[/math] |
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