K12n732
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-13 q^6+17 q^5-19 q^4+19 q^3-15 q^2+11 q-6+2 q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+28 t-39+28 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-4} -3 z^4 a^{-2} +2 z^4 a^{-4} -2 z^4 a^{-6} -4 z^2 a^{-2} +4 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} +2 z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-4} +3 z^{10} a^{-6} +6 z^9 a^{-3} +13 z^9 a^{-5} +7 z^9 a^{-7} +4 z^8 a^{-2} -z^8 a^{-4} +2 z^8 a^{-6} +7 z^8 a^{-8} +z^7 a^{-1} -18 z^7 a^{-3} -41 z^7 a^{-5} -18 z^7 a^{-7} +4 z^7 a^{-9} -6 z^6 a^{-2} -9 z^6 a^{-4} -23 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} +5 z^5 a^{-1} +33 z^5 a^{-3} +51 z^5 a^{-5} +13 z^5 a^{-7} -10 z^5 a^{-9} +9 z^4 a^{-2} +19 z^4 a^{-4} +28 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} +3 z^4-9 z^3 a^{-1} -24 z^3 a^{-3} -23 z^3 a^{-5} -4 z^3 a^{-7} +4 z^3 a^{-9} -8 z^2 a^{-2} -10 z^2 a^{-4} -10 z^2 a^{-6} -4 z^2 a^{-8} -4 z^2+2 z a^{-1} +5 z a^{-3} +3 z a^{-5} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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