K12a690
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+4 q^6-7 q^5+10 q^4-12 q^3+13 q^2-13 q+11-8 q^{-1} +5 q^{-2} -2 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-22 t+37-22 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4-6 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4-2 z^2 a^2+z^4-2 z^2-1+2 z^4 a^{-2} +z^2 a^{-2} + a^{-2} +z^4 a^{-4} -z^2 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} -2 z^8 a^{-2} -16 z^8 a^{-4} -9 z^8 a^{-6} +z^8 a^{-8} +4 z^8+4 a z^7-2 z^7 a^{-1} +2 z^7 a^{-3} -3 z^7 a^{-5} -11 z^7 a^{-7} +3 a^2 z^6-z^6 a^{-2} +24 z^6 a^{-4} +11 z^6 a^{-6} -6 z^6 a^{-8} -5 z^6+2 a^3 z^5-5 a z^5-7 z^5 a^{-1} -13 z^5 a^{-3} +6 z^5 a^{-5} +19 z^5 a^{-7} +a^4 z^4-2 a^2 z^4-5 z^4 a^{-2} -22 z^4 a^{-4} -2 z^4 a^{-6} +11 z^4 a^{-8} +z^4-2 a^3 z^3+5 a z^3+9 z^3 a^{-1} +10 z^3 a^{-3} -3 z^3 a^{-5} -11 z^3 a^{-7} -2 a^4 z^2+5 z^2 a^{-2} +7 z^2 a^{-4} -2 z^2 a^{-6} -6 z^2 a^{-8} +4 z^2-2 a z-2 z a^{-1} -2 z a^{-3} +2 z a^{-7} +a^4- a^{-2} + a^{-6} + a^{-8} -1 }[/math] |
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