K12a251
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-14 q^6+20 q^5-23 q^4+25 q^3-23 q^2+18 q-12+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+38 t-51+38 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4+1 }[/math] |
| Determinant | 159 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} +z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2+z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} -3 z^2+a^2+2 a^{-4} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +4 z^9 a^{-1} +8 z^9 a^{-3} +11 z^9 a^{-5} +7 z^9 a^{-7} -10 z^8 a^{-4} +z^8 a^{-6} +7 z^8 a^{-8} +4 z^8+3 a z^7-3 z^7 a^{-1} -21 z^7 a^{-3} -33 z^7 a^{-5} -14 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-3 z^6 a^{-2} +2 z^6 a^{-4} -21 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -6 z^6-8 a z^5-5 z^5 a^{-1} +27 z^5 a^{-3} +39 z^5 a^{-5} +5 z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4-2 z^4 a^{-2} +11 z^4 a^{-4} +28 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} -3 z^4+6 a z^3+2 z^3 a^{-1} -19 z^3 a^{-3} -18 z^3 a^{-5} +2 z^3 a^{-7} +5 z^3 a^{-9} +3 a^2 z^2+z^2 a^{-2} -10 z^2 a^{-4} -12 z^2 a^{-6} -4 z^2 a^{-8} +6 z^2-a z+z a^{-1} +5 z a^{-3} +3 z a^{-5} -a^2+2 a^{-4} + a^{-6} -1 }[/math] |
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