K12a585
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-8 q^5+14 q^4-21 q^3+26 q^2-28 q+27-22 q^{-1} +16 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-43 t+61-43 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4-z^2+1 }[/math] |
| Determinant | 181 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+2 a^2 z^4-z^4 a^{-2} +2 z^4 a^{-4} -a^4 z^2+a^2 z^2-3 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+8 a z^9+15 z^9 a^{-1} +13 z^9 a^{-3} +6 z^9 a^{-5} +10 a^2 z^8-4 z^8 a^{-2} -2 z^8 a^{-4} +4 z^8 a^{-6} +12 z^8+8 a^3 z^7-a z^7-30 z^7 a^{-1} -41 z^7 a^{-3} -19 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-12 a^2 z^6-25 z^6 a^{-2} -20 z^6 a^{-4} -14 z^6 a^{-6} -35 z^6+a^5 z^5-11 a^3 z^5-15 a z^5+13 z^5 a^{-1} +37 z^5 a^{-3} +18 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+5 a^2 z^4+29 z^4 a^{-2} +26 z^4 a^{-4} +14 z^4 a^{-6} +27 z^4-a^5 z^3+6 a^3 z^3+12 a z^3-z^3 a^{-1} -13 z^3 a^{-3} -5 z^3 a^{-5} +2 z^3 a^{-7} +2 a^4 z^2-a^2 z^2-13 z^2 a^{-2} -9 z^2 a^{-4} -3 z^2 a^{-6} -10 z^2-a^3 z-2 a z+z a^{-3} +2 a^{-2} + a^{-4} +2 }[/math] |
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