K12a650
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+15 q^2-21 q+25-25 q^{-1} +24 q^{-2} -18 q^{-3} +12 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-39 t+53-39 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+3 z^2 a^4+a^4-z^6 a^2-z^4 a^2-z^2 a^2-z^6+2 z^2+2+2 z^4 a^{-2} +z^2 a^{-2} - a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+7 a^2 z^{10}+4 z^{10}+4 a^5 z^9+8 a^3 z^9+12 a z^9+8 z^9 a^{-1} +3 a^6 z^8-2 a^4 z^8-8 a^2 z^8+10 z^8 a^{-2} +7 z^8+a^7 z^7-11 a^5 z^7-26 a^3 z^7-28 a z^7-6 z^7 a^{-1} +8 z^7 a^{-3} -11 a^6 z^6-12 a^4 z^6-7 a^2 z^6-15 z^6 a^{-2} +4 z^6 a^{-4} -25 z^6-4 a^7 z^5+6 a^5 z^5+26 a^3 z^5+24 a z^5-5 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+15 a^4 z^4+12 a^2 z^4+9 z^4 a^{-2} -5 z^4 a^{-4} +23 z^4+5 a^7 z^3+2 a^5 z^3-16 a^3 z^3-14 a z^3+6 z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2-6 a^4 z^2-8 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} -10 z^2-2 a^7 z+5 a^3 z+4 a z-z a^{-3} +a^6+a^4+ a^{-2} +2 }[/math] |
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