K12a401
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+13 q^5-18 q^4+23 q^3-25 q^2+23 q-19+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/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^2 z^4-3 z^4 a^{-4} +2 z^4-a^2 z^2-2 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2-2 a^{-2} +2 a^{-6} - a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+6 a z^9+13 z^9 a^{-1} +13 z^9 a^{-3} +6 z^9 a^{-5} +4 a^2 z^8-11 z^8 a^{-2} +z^8 a^{-4} +6 z^8 a^{-6} -2 z^8+a^3 z^7-19 a z^7-51 z^7 a^{-1} -42 z^7 a^{-3} -6 z^7 a^{-5} +5 z^7 a^{-7} -14 a^2 z^6-17 z^6 a^{-2} -12 z^6 a^{-4} -5 z^6 a^{-6} +3 z^6 a^{-8} -27 z^6-3 a^3 z^5+16 a z^5+60 z^5 a^{-1} +52 z^5 a^{-3} +4 z^5 a^{-5} -6 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+36 z^4 a^{-2} +14 z^4 a^{-4} -2 z^4 a^{-6} -5 z^4 a^{-8} +39 z^4+2 a^3 z^3-6 a z^3-32 z^3 a^{-1} -32 z^3 a^{-3} -5 z^3 a^{-5} +z^3 a^{-7} -2 z^3 a^{-9} -5 a^2 z^2-19 z^2 a^{-2} -6 z^2 a^{-4} +4 z^2 a^{-6} +3 z^2 a^{-8} -17 z^2+2 a z+8 z a^{-1} +9 z a^{-3} +3 z a^{-5} +z a^{-7} +z a^{-9} +2 a^{-2} -2 a^{-6} - a^{-8} +2 }[/math] |
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