K12a471
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+4 q^4-7 q^3+10 q^2-12 q+13-12 q^{-1} +10 q^{-2} -7 q^{-3} +4 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-21 t+35-21 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4-5 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-2 z^2 a^4-a^4+z^4 a^2-z^2 a^2+2 z^4+z^2+1+z^4 a^{-2} -z^2 a^{-2} -2 z^2 a^{-4} - a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+2 a^3 z^9-2 a z^9-2 z^9 a^{-1} +2 z^9 a^{-3} +2 a^4 z^8-7 a^2 z^8-7 z^8 a^{-2} +2 z^8 a^{-4} -18 z^8+2 a^5 z^7-4 a^3 z^7-4 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-4 a^4 z^6+12 a^2 z^6+12 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +34 z^6-7 a^5 z^5-a^3 z^5+7 a z^5+7 z^5 a^{-1} -z^5 a^{-3} -7 z^5 a^{-5} -4 a^6 z^4-3 a^4 z^4-9 a^2 z^4-9 z^4 a^{-2} -3 z^4 a^{-4} -4 z^4 a^{-6} -20 z^4+6 a^5 z^3+4 a^3 z^3-3 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} +6 z^3 a^{-5} +4 a^6 z^2+5 a^4 z^2+2 a^2 z^2+2 z^2 a^{-2} +5 z^2 a^{-4} +4 z^2 a^{-6} +2 z^2-2 a^5 z-2 a^3 z-a z-z a^{-1} -2 z a^{-3} -2 z a^{-5} -a^6-a^4- a^{-4} - a^{-6} +1 }[/math] |
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