K12a233
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+11 q^4-20 q^3+29 q^2-37 q+40-37 q^{-1} +31 q^{-2} -21 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+27 t^2-54 t+69-54 t^{-1} +27 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^4-2 z^2+1 }[/math] |
| Determinant | 249 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-5 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +8 z^4+a^4 z^2-4 a^2 z^2-8 z^2 a^{-2} +2 z^2 a^{-4} +7 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +8 a^2 z^{10}+7 z^{10} a^{-2} +15 z^{10}+13 a^3 z^9+27 a z^9+25 z^9 a^{-1} +11 z^9 a^{-3} +11 a^4 z^8+9 a^2 z^8+10 z^8 a^{-2} +9 z^8 a^{-4} -z^8+5 a^5 z^7-19 a^3 z^7-60 a z^7-56 z^7 a^{-1} -16 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-48 a^2 z^6-49 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} -56 z^6-8 a^5 z^5+3 a^3 z^5+35 a z^5+37 z^5 a^{-1} +6 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+43 a^2 z^4+54 z^4 a^{-2} +16 z^4 a^{-4} -2 z^4 a^{-6} +65 z^4+3 a^5 z^3+3 a^3 z^3-5 a z^3-10 z^3 a^{-1} -z^3 a^{-3} +4 z^3 a^{-5} -3 a^4 z^2-13 a^2 z^2-26 z^2 a^{-2} -9 z^2 a^{-4} +z^2 a^{-6} -26 z^2+a z+3 z a^{-1} +z a^{-3} -z a^{-5} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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