K12n493
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+9 q^2-12 q+15-16 q^{-1} +14 q^{-2} -11 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+9 t^2-21 t+29-21 t^{-1} +9 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-3 z^4-3 z^2+1 }[/math] |
| Determinant | 93 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6+a^4 z^4-3 a^2 z^4+z^4 a^{-2} -2 z^4+2 a^4 z^2-5 a^2 z^2+z^2 a^{-2} -z^2+2 a^4-3 a^2+ a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+4 a^3 z^9+6 a z^9+2 z^9 a^{-1} +5 a^4 z^8+8 a^2 z^8+z^8 a^{-2} +4 z^8+3 a^5 z^7-7 a^3 z^7-11 a z^7-z^7 a^{-1} +a^6 z^6-14 a^4 z^6-28 a^2 z^6+3 z^6 a^{-2} -10 z^6-8 a^5 z^5+a^3 z^5+8 a z^5+3 z^5 a^{-1} +4 z^5 a^{-3} -3 a^6 z^4+13 a^4 z^4+32 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} +13 z^4+5 a^5 z^3-a^3 z^3-4 a z^3-z^3 a^{-1} -3 z^3 a^{-3} +2 a^6 z^2-8 a^4 z^2-18 a^2 z^2-z^2 a^{-4} -7 z^2-a^5 z+a^3 z+2 a z+2 a^4+3 a^2- a^{-2} +1 }[/math] |
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