K12a691
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+4 q^6-6 q^5+8 q^4-10 q^3+11 q^2-11 q+9-7 q^{-1} +5 q^{-2} -2 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^2-19 t+33-19 t^{-1} +3 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^4-7 z^2+1 }[/math] |
| Determinant | 77 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4-2 z^2 a^2+z^4-z^2+z^4 a^{-2} -2 z^2 a^{-2} - a^{-2} +z^4 a^{-4} + a^{-4} -2 z^2 a^{-6} - a^{-6} + 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} +3 z^9 a^{-1} -z^9 a^{-3} -2 z^9 a^{-5} +2 z^9 a^{-7} -4 z^8 a^{-2} -17 z^8 a^{-4} -9 z^8 a^{-6} +z^8 a^{-8} +3 z^8+3 a z^7-8 z^7 a^{-1} -5 z^7 a^{-3} -5 z^7 a^{-5} -11 z^7 a^{-7} +3 a^2 z^6-2 z^6 a^{-2} +20 z^6 a^{-4} +9 z^6 a^{-6} -6 z^6 a^{-8} -4 z^6+2 a^3 z^5-2 a z^5+12 z^5 a^{-1} +5 z^5 a^{-3} +7 z^5 a^{-5} +18 z^5 a^{-7} +a^4 z^4-3 a^2 z^4+9 z^4 a^{-2} -8 z^4 a^{-4} +z^4 a^{-6} +11 z^4 a^{-8} +3 z^4-2 a^3 z^3-11 z^3 a^{-1} -z^3 a^{-3} +2 z^3 a^{-5} -10 z^3 a^{-7} -2 a^4 z^2+a^2 z^2-8 z^2 a^{-2} -3 z^2 a^{-6} -7 z^2 a^{-8} -z^2+3 z a^{-1} -2 z a^{-5} +z a^{-7} +a^4+ a^{-2} + a^{-4} + a^{-6} + a^{-8} }[/math] |
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