K12a438
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-11 q^3+19 q^2-27 q+32-33 q^{-1} +30 q^{-2} -23 q^{-3} +16 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+25 t^2-44 t+53-44 t^{-1} +25 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-3 z^4+1 }[/math] |
| Determinant | 209 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-10 a^2 z^4-2 z^4 a^{-2} +6 z^4-a^6 z^2+8 a^4 z^2-10 a^2 z^2+3 z^2-2 a^6+5 a^4-3 a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+13 a^2 z^{10}+8 z^{10}+5 a^5 z^9+11 a^3 z^9+20 a z^9+14 z^9 a^{-1} +3 a^6 z^8-7 a^4 z^8-21 a^2 z^8+15 z^8 a^{-2} +4 z^8+a^7 z^7-13 a^5 z^7-41 a^3 z^7-53 a z^7-15 z^7 a^{-1} +11 z^7 a^{-3} -10 a^6 z^6-8 a^4 z^6-4 a^2 z^6-19 z^6 a^{-2} +5 z^6 a^{-4} -30 z^6-4 a^7 z^5+8 a^5 z^5+41 a^3 z^5+39 a z^5-4 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+18 a^4 z^4+20 a^2 z^4+3 z^4 a^{-2} -4 z^4 a^{-4} +20 z^4+5 a^7 z^3+a^5 z^3-15 a^3 z^3-6 a z^3+8 z^3 a^{-1} +3 z^3 a^{-3} -6 a^6 z^2-15 a^4 z^2-12 a^2 z^2+3 z^2 a^{-2} -2 a^7 z-2 a^5 z-2 a z-2 z a^{-1} +2 a^6+5 a^4+3 a^2- a^{-2} }[/math] |
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