K12a229
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+11 q^4-18 q^3+26 q^2-30 q+32-29 q^{-1} +22 q^{-2} -15 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+16 t^2-48 t+69-48 t^{-1} +16 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+4 z^4-2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-a^4+3 z^4 a^2+z^2 a^2-a^2-z^6+z^4+2 z^2+2-z^6 a^{-2} -z^4 a^{-2} -2 z^2 a^{-2} +z^4 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+5 z^{10} a^{-2} +9 z^{10}+6 a^3 z^9+17 a z^9+21 z^9 a^{-1} +10 z^9 a^{-3} +5 a^4 z^8+5 a^2 z^8+13 z^8 a^{-2} +10 z^8 a^{-4} +3 z^8+3 a^5 z^7-8 a^3 z^7-43 a z^7-50 z^7 a^{-1} -13 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-8 a^4 z^6-22 a^2 z^6-55 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -46 z^6-7 a^5 z^5+5 a^3 z^5+49 a z^5+40 z^5 a^{-1} -6 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4+a^4 z^4+24 a^2 z^4+54 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +61 z^4+5 a^5 z^3-7 a^3 z^3-32 a z^3-16 z^3 a^{-1} +7 z^3 a^{-3} +3 z^3 a^{-5} +3 a^6 z^2+3 a^4 z^2-12 a^2 z^2-18 z^2 a^{-2} -3 z^2 a^{-4} -27 z^2-a^5 z+4 a^3 z+10 a z+6 z a^{-1} +z a^{-3} -a^6-a^4+a^2+2 }[/math] |
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