K12a403
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+18 q^4-25 q^3+31 q^2-33 q+31-25 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+19 t^2-49 t+67-49 t^{-1} +19 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+z^4+1 }[/math] |
| Determinant | 209 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-5 z^4 a^{-2} +3 z^4 a^{-4} +z^4-a^4 z^2+a^2 z^2-7 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +3 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +6 z^{10} a^{-4} +7 z^{10}+11 a z^9+19 z^9 a^{-1} +15 z^9 a^{-3} +7 z^9 a^{-5} +11 a^2 z^8-15 z^8 a^{-2} -5 z^8 a^{-4} +4 z^8 a^{-6} +5 z^8+8 a^3 z^7-10 a z^7-49 z^7 a^{-1} -50 z^7 a^{-3} -18 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-13 a^2 z^6-25 z^6 a^{-2} -22 z^6 a^{-4} -12 z^6 a^{-6} -32 z^6+a^5 z^5-10 a^3 z^5-4 a z^5+32 z^5 a^{-1} +39 z^5 a^{-3} +11 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+5 a^2 z^4+39 z^4 a^{-2} +30 z^4 a^{-4} +12 z^4 a^{-6} +31 z^4-a^5 z^3+5 a^3 z^3+9 a z^3-3 z^3 a^{-1} -9 z^3 a^{-3} +3 z^3 a^{-7} +2 a^4 z^2-18 z^2 a^{-2} -14 z^2 a^{-4} -5 z^2 a^{-6} -11 z^2-a^3 z-3 a z-2 z a^{-1} -z a^{-5} -z a^{-7} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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