K12n547
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+4 q^2-6 q+9-11 q^{-1} +11 q^{-2} -10 q^{-3} +8 q^{-4} -5 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-17 t+27-17 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4-z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+z^4 a^4+2 z^4 a^2+2 z^2 a^2+a^2+z^4-z^2-1-z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+3 a^5 z^9+5 a^3 z^9+2 a z^9+3 a^6 z^8+2 a^4 z^8+a^2 z^8+2 z^8+a^7 z^7-11 a^5 z^7-16 a^3 z^7-3 a z^7+z^7 a^{-1} -13 a^6 z^6-16 a^4 z^6-5 a^2 z^6-2 z^6-4 a^7 z^5+11 a^5 z^5+18 a^3 z^5+5 a z^5+2 z^5 a^{-1} +16 a^6 z^4+17 a^4 z^4+4 z^4 a^{-2} +3 z^4+4 a^7 z^3-5 a^5 z^3-16 a^3 z^3-9 a z^3-z^3 a^{-1} +z^3 a^{-3} -5 a^6 z^2-6 a^4 z^2+a^2 z^2-2 z^2 a^{-2} +2 a^5 z+6 a^3 z+5 a z+z a^{-1} -a^2- a^{-2} -1 }[/math] |
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