K12a1154
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+8 q^7-15 q^6+22 q^5-29 q^4+31 q^3-29 q^2+25 q-17+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-17 t^2+47 t-63+47 t^{-1} -17 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-5 z^4-3 z^2+1 }[/math] |
| Determinant | 195 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} -z^4 a^{-2} -2 z^4 a^{-6} -2 z^4+a^2 z^2-3 z^2 a^{-2} -2 z^2 a^{-6} +z^2 a^{-8} - a^{-2} - a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +12 z^{10} a^{-4} +6 z^{10} a^{-6} +9 z^9 a^{-1} +13 z^9 a^{-3} +12 z^9 a^{-5} +8 z^9 a^{-7} -21 z^8 a^{-4} -7 z^8 a^{-6} +6 z^8 a^{-8} +8 z^8+4 a z^7-15 z^7 a^{-1} -37 z^7 a^{-3} -42 z^7 a^{-5} -21 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-20 z^6 a^{-2} +9 z^6 a^{-4} -5 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -17 z^6-8 a z^5+6 z^5 a^{-1} +38 z^5 a^{-3} +59 z^5 a^{-5} +28 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+21 z^4 a^{-2} +9 z^4 a^{-4} +19 z^4 a^{-6} +14 z^4 a^{-8} -3 z^4 a^{-10} +12 z^4+4 a z^3-4 z^3 a^{-1} -21 z^3 a^{-3} -38 z^3 a^{-5} -22 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2-11 z^2 a^{-2} -6 z^2 a^{-4} -12 z^2 a^{-6} -8 z^2 a^{-8} +2 z^2 a^{-10} -6 z^2+z a^{-1} +6 z a^{-3} +12 z a^{-5} +7 z a^{-7} + a^{-2} + a^{-6} + a^{-8} +2 }[/math] |
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