K12a68
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-8 q^3+15 q^2-22 q+27-29 q^{-1} +27 q^{-2} -22 q^{-3} +16 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-44 t+63-44 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4-2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+2 z^4 a^4+z^2 a^4-z^6 a^2+z^2 a^2+2 a^2-z^6-z^4-4 z^2-3+2 z^4 a^{-2} +2 z^2 a^{-2} +2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+12 a^2 z^{10}+6 z^{10}+7 a^5 z^9+11 a^3 z^9+12 a z^9+8 z^9 a^{-1} +4 a^6 z^8-11 a^4 z^8-25 a^2 z^8+8 z^8 a^{-2} -2 z^8+a^7 z^7-22 a^5 z^7-47 a^3 z^7-35 a z^7-4 z^7 a^{-1} +7 z^7 a^{-3} -13 a^6 z^6-7 a^4 z^6+9 a^2 z^6-4 z^6 a^{-2} +4 z^6 a^{-4} -5 z^6-3 a^7 z^5+20 a^5 z^5+49 a^3 z^5+26 a z^5-10 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+16 a^4 z^4+3 a^2 z^4-10 z^4 a^{-2} -6 z^4 a^{-4} -5 z^4+2 a^7 z^3-8 a^5 z^3-18 a^3 z^3-2 a z^3+11 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2-6 a^4 z^2+3 a^2 z^2+9 z^2 a^{-2} +3 z^2 a^{-4} +11 z^2+a^5 z+2 a^3 z-2 a z-4 z a^{-1} -z a^{-3} -2 a^2-2 a^{-2} -3 }[/math] |
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