K12a555
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-11 q^5+18 q^4-25 q^3+29 q^2-30 q+28-21 q^{-1} +14 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+18 t^2-45 t+61-45 t^{-1} +18 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-3 z^6 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-5 z^4 a^{-2} +3 z^4 a^{-4} -a^4 z^2+3 a^2 z^2-6 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +z^2-a^4+2 a^2-2 a^{-2} + a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +7 z^{10} a^{-4} +6 z^{10}+8 a z^9+15 z^9 a^{-1} +16 z^9 a^{-3} +9 z^9 a^{-5} +7 a^2 z^8-22 z^8 a^{-2} -9 z^8 a^{-4} +5 z^8 a^{-6} -z^8+5 a^3 z^7-10 a z^7-48 z^7 a^{-1} -60 z^7 a^{-3} -26 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-7 a^2 z^6-11 z^6 a^{-2} -19 z^6 a^{-4} -14 z^6 a^{-6} -16 z^6+a^5 z^5-5 a^3 z^5+6 a z^5+45 z^5 a^{-1} +54 z^5 a^{-3} +19 z^5 a^{-5} -2 z^5 a^{-7} -5 a^4 z^4+a^2 z^4+30 z^4 a^{-2} +25 z^4 a^{-4} +10 z^4 a^{-6} +21 z^4-2 a^5 z^3-13 z^3 a^{-1} -15 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} +3 a^4 z^2+3 a^2 z^2-14 z^2 a^{-2} -8 z^2 a^{-4} -z^2 a^{-6} -7 z^2+a^5 z+a^3 z-z a^{-3} -z a^{-5} -a^4-2 a^2+2 a^{-2} + a^{-4} +1 }[/math] |
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