K12a1275
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-12 q^3+18 q^2-22 q+23-22 q^{-1} +18 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-33 t+43-33 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4-5 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-2 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -6 z^4+2 a^4 z^2-a^2 z^2-z^2 a^{-2} +2 z^2 a^{-4} -7 z^2+a^4+a^2+ a^{-2} + a^{-4} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+5 a^3 z^9+6 a z^9+6 z^9 a^{-1} +5 z^9 a^{-3} +5 a^4 z^8+5 z^8 a^{-4} -10 z^8+3 a^5 z^7-10 a^3 z^7-12 a z^7-12 z^7 a^{-1} -10 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-13 a^4 z^6-6 a^2 z^6-6 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} +16 z^6-8 a^5 z^5+9 a^3 z^5+10 a z^5+10 z^5 a^{-1} +9 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+12 a^4 z^4+4 a^2 z^4+4 z^4 a^{-2} +12 z^4 a^{-4} -3 z^4 a^{-6} -22 z^4+5 a^5 z^3-7 a^3 z^3-5 a z^3-5 z^3 a^{-1} -7 z^3 a^{-3} +5 z^3 a^{-5} +2 a^6 z^2-6 a^4 z^2-6 z^2 a^{-4} +2 z^2 a^{-6} +16 z^2+2 a^3 z+a z+z a^{-1} +2 z a^{-3} +a^4-a^2- a^{-2} + a^{-4} -3 }[/math] |
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