K12n783
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+10 q^7-16 q^6+20 q^5-21 q^4+21 q^3-16 q^2+11 q-5+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-11 t^2+30 t-41+30 t^{-1} -11 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-4} -3 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4 a^{-6} -4 z^2 a^{-2} +11 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +z^2- a^{-2} +5 a^{-4} -3 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +4 z^9 a^{-3} +11 z^9 a^{-5} +7 z^9 a^{-7} +2 z^8 a^{-2} +7 z^8 a^{-4} +14 z^8 a^{-6} +9 z^8 a^{-8} -5 z^7 a^{-3} -16 z^7 a^{-5} -6 z^7 a^{-7} +5 z^7 a^{-9} +z^6 a^{-2} -21 z^6 a^{-4} -43 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +5 z^5 a^{-1} +7 z^5 a^{-3} -5 z^5 a^{-5} -17 z^5 a^{-7} -10 z^5 a^{-9} +4 z^4 a^{-2} +25 z^4 a^{-4} +33 z^4 a^{-6} +10 z^4 a^{-8} -z^4 a^{-10} +z^4-3 z^3 a^{-1} +3 z^3 a^{-3} +17 z^3 a^{-5} +15 z^3 a^{-7} +4 z^3 a^{-9} -4 z^2 a^{-2} -14 z^2 a^{-4} -13 z^2 a^{-6} -2 z^2 a^{-8} -z^2-z a^{-1} -4 z a^{-3} -8 z a^{-5} -4 z a^{-7} +z a^{-9} + a^{-2} +5 a^{-4} +3 a^{-6} }[/math] |
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