K12a593
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-16 q^3+23 q^2-27 q+29-26 q^{-1} +21 q^{-2} -14 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+19 t^2-41 t+53-41 t^{-1} +19 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-5 z^4-z^2+1 }[/math] |
| Determinant | 181 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-2 a^2 z^4-z^4 a^{-2} +z^4 a^{-4} -4 z^4+2 a^4 z^2-3 a^2 z^2+z^2 a^{-4} -z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+6 z^{10} a^{-2} +11 z^{10}+6 a^3 z^9+7 a z^9+9 z^9 a^{-1} +8 z^9 a^{-3} +5 a^4 z^8-6 a^2 z^8-7 z^8 a^{-2} +7 z^8 a^{-4} -25 z^8+3 a^5 z^7-11 a^3 z^7-23 a z^7-27 z^7 a^{-1} -14 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-11 a^4 z^6+3 z^6 a^{-2} -14 z^6 a^{-4} +z^6 a^{-6} +30 z^6-8 a^5 z^5+5 a^3 z^5+28 a z^5+30 z^5 a^{-1} +6 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4+7 a^4 z^4+7 a^2 z^4-6 z^4 a^{-2} +6 z^4 a^{-4} -2 z^4 a^{-6} -17 z^4+6 a^5 z^3+3 a^3 z^3-11 a z^3-16 z^3 a^{-1} -3 z^3 a^{-3} +5 z^3 a^{-5} +2 a^6 z^2-3 a^4 z^2-6 a^2 z^2+2 z^2 a^{-2} +z^2 a^{-6} +2 z^2-2 a^5 z-3 a^3 z+2 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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