K12a943
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-18 q^3+27 q^2-33 q+35-33 q^{-1} +27 q^{-2} -18 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+21 t^2-51 t+69-51 t^{-1} +21 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-3 z^4-3 z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-a^2 z^4-z^4 a^{-2} +z^4 a^{-4} -3 z^4+a^4 z^2-2 a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} -z^2+a^4-a^2- a^{-2} + a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+9 z^{10} a^{-2} +17 z^{10}+10 a^3 z^9+13 a z^9+15 z^9 a^{-1} +12 z^9 a^{-3} +8 a^4 z^8-8 a^2 z^8-12 z^8 a^{-2} +9 z^8 a^{-4} -37 z^8+4 a^5 z^7-18 a^3 z^7-42 a z^7-54 z^7 a^{-1} -30 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-2 a^2 z^6-5 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} +33 z^6-8 a^5 z^5+12 a^3 z^5+49 a z^5+67 z^5 a^{-1} +30 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+10 a^4 z^4+3 a^2 z^4+19 z^4 a^{-2} +18 z^4 a^{-4} -2 z^4 a^{-6} -10 z^4+4 a^5 z^3-8 a^3 z^3-30 a z^3-34 z^3 a^{-1} -14 z^3 a^{-3} +2 z^3 a^{-5} +a^6 z^2-3 a^4 z^2-4 a^2 z^2-9 z^2 a^{-2} -7 z^2 a^{-4} -2 z^2+3 a^3 z+6 a z+6 z a^{-1} +3 z a^{-3} +a^4+a^2+ a^{-2} + a^{-4} +1 }[/math] |
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