K12n489
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^8+6 q^7-11 q^6+16 q^5-19 q^4+20 q^3-18 q^2+14 q-8+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-11 t^2+28 t-37+28 t^{-1} -11 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +2 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} -z^4+3 z^2 a^{-2} -z^2 a^{-4} +z^2 a^{-6} -z^2+2 a^{-2} -2 a^{-4} +2 a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +4 z^9 a^{-3} +6 z^9 a^{-5} +2 z^9 a^{-7} +7 z^8 a^{-2} +12 z^8 a^{-4} +6 z^8 a^{-6} +z^8 a^{-8} +7 z^7 a^{-1} +8 z^7 a^{-3} +3 z^7 a^{-5} +2 z^7 a^{-7} -4 z^6 a^{-2} -17 z^6 a^{-4} -5 z^6 a^{-6} +4 z^6 a^{-8} +4 z^6+a z^5-10 z^5 a^{-1} -25 z^5 a^{-3} -22 z^5 a^{-5} -5 z^5 a^{-7} +3 z^5 a^{-9} -8 z^4 a^{-2} -3 z^4 a^{-4} -11 z^4 a^{-6} -10 z^4 a^{-8} -6 z^4-a z^3+5 z^3 a^{-1} +17 z^3 a^{-3} +15 z^3 a^{-5} -z^3 a^{-7} -5 z^3 a^{-9} +8 z^2 a^{-2} +9 z^2 a^{-4} +10 z^2 a^{-6} +6 z^2 a^{-8} +3 z^2-z a^{-1} -3 z a^{-3} -3 z a^{-5} +z a^{-7} +2 z a^{-9} -2 a^{-2} -2 a^{-4} -2 a^{-6} - a^{-8} }[/math] |
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