K12a883
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+9 q^2-16 q+23-27 q^{-1} +29 q^{-2} -26 q^{-3} +22 q^{-4} -15 q^{-5} +8 q^{-6} -4 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-42 t+53-42 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^6+z^2 a^6-a^6-z^6 a^4-z^4 a^4+z^2 a^4+a^4-2 z^6 a^2-4 z^4 a^2-z^2 a^2+a^2-z^6-z^4+z^4 a^{-2} +z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+6 a^6 z^{10}+16 a^4 z^{10}+10 a^2 z^{10}+4 a^7 z^9+a^5 z^9+14 a^3 z^9+17 a z^9+a^8 z^8-25 a^6 z^8-55 a^4 z^8-10 a^2 z^8+19 z^8-18 a^7 z^7-38 a^5 z^7-68 a^3 z^7-33 a z^7+15 z^7 a^{-1} -4 a^8 z^6+34 a^6 z^6+56 a^4 z^6-26 a^2 z^6+9 z^6 a^{-2} -35 z^6+26 a^7 z^5+63 a^5 z^5+73 a^3 z^5+13 a z^5-19 z^5 a^{-1} +4 z^5 a^{-3} +4 a^8 z^4-18 a^6 z^4-22 a^4 z^4+27 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +20 z^4-12 a^7 z^3-33 a^5 z^3-31 a^3 z^3-2 a z^3+7 z^3 a^{-1} -z^3 a^{-3} +3 a^6 z^2+3 a^4 z^2-5 a^2 z^2+z^2 a^{-2} -4 z^2+4 a^5 z+6 a^3 z+2 a z+a^6+a^4-a^2 }[/math] |
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