K12a856
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-18 q^3+27 q^2-34 q+37-35 q^{-1} +29 q^{-2} -20 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+22 t^2-54 t+73-54 t^{-1} +22 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 233 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-z^4 a^{-2} +z^4 a^{-4} -3 z^4+a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} -2 z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +9 a^2 z^{10}+9 z^{10} a^{-2} +18 z^{10}+13 a^3 z^9+18 a z^9+17 z^9 a^{-1} +12 z^9 a^{-3} +11 a^4 z^8-4 a^2 z^8-11 z^8 a^{-2} +9 z^8 a^{-4} -35 z^8+5 a^5 z^7-23 a^3 z^7-53 a z^7-59 z^7 a^{-1} -30 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-18 a^2 z^6-7 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} +21 z^6-8 a^5 z^5+9 a^3 z^5+49 a z^5+71 z^5 a^{-1} +31 z^5 a^{-3} -8 z^5 a^{-5} -a^6 z^4+11 a^4 z^4+12 a^2 z^4+22 z^4 a^{-2} +18 z^4 a^{-4} -2 z^4 a^{-6} +2 z^4+2 a^5 z^3-2 a^3 z^3-20 a z^3-33 z^3 a^{-1} -15 z^3 a^{-3} +2 z^3 a^{-5} -a^4 z^2-11 z^2 a^{-2} -7 z^2 a^{-4} -3 z^2+a^3 z+3 a z+5 z a^{-1} +3 z a^{-3} -a^2+ a^{-2} + a^{-4} }[/math] |
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