K12a666
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+11 q^7-19 q^6+26 q^5-32 q^4+33 q^3-30 q^2+24 q-15+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-20 t^2+49 t-63+49 t^{-1} -20 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-2 z^4-4 z^2+1 }[/math] |
| Determinant | 207 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2- a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10} a^{-6} +6 z^9 a^{-1} +11 z^9 a^{-3} +16 z^9 a^{-5} +11 z^9 a^{-7} -14 z^8 a^{-4} +9 z^8 a^{-8} +5 z^8+3 a z^7-6 z^7 a^{-1} -23 z^7 a^{-3} -39 z^7 a^{-5} -21 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-10 z^6 a^{-2} -4 z^6 a^{-4} -23 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} -8 z^6-7 a z^5-3 z^5 a^{-1} +11 z^5 a^{-3} +29 z^5 a^{-5} +15 z^5 a^{-7} -7 z^5 a^{-9} -3 a^2 z^4+10 z^4 a^{-2} +11 z^4 a^{-4} +23 z^4 a^{-6} +15 z^4 a^{-8} -2 z^4 a^{-10} +2 z^4+5 a z^3+6 z^3 a^{-1} +5 z^3 a^{-3} -10 z^3 a^{-5} -11 z^3 a^{-7} +3 z^3 a^{-9} +3 a^2 z^2-4 z^2 a^{-2} -3 z^2 a^{-4} -10 z^2 a^{-6} -8 z^2 a^{-8} +z^2 a^{-10} +z^2-a z-3 z a^{-1} -3 z a^{-3} +3 z a^{-5} +4 z a^{-7} -a^2+ a^{-6} + a^{-8} }[/math] |
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