K12a635
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+16 q^2-24 q+30-31 q^{-1} +30 q^{-2} -24 q^{-3} +17 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+19 t^2-47 t+63-47 t^{-1} +19 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+3 z^4 a^4+5 z^2 a^4+2 a^4-2 z^6 a^2-5 z^4 a^2-6 z^2 a^2-2 a^2-z^6+z^4+4 z^2+3+2 z^4 a^{-2} +z^2 a^{-2} - a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+13 a^2 z^{10}+7 z^{10}+7 a^5 z^9+14 a^3 z^9+18 a z^9+11 z^9 a^{-1} +4 a^6 z^8-7 a^4 z^8-20 a^2 z^8+11 z^8 a^{-2} +2 z^8+a^7 z^7-19 a^5 z^7-52 a^3 z^7-54 a z^7-14 z^7 a^{-1} +8 z^7 a^{-3} -12 a^6 z^6-17 a^4 z^6-15 a^2 z^6-16 z^6 a^{-2} +4 z^6 a^{-4} -30 z^6-3 a^7 z^5+13 a^5 z^5+50 a^3 z^5+49 a z^5+3 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+25 a^4 z^4+37 a^2 z^4+10 z^4 a^{-2} -5 z^4 a^{-4} +38 z^4+3 a^7 z^3-3 a^5 z^3-21 a^3 z^3-16 a z^3+5 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2-12 a^4 z^2-20 a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} -17 z^2-a^7 z+a^5 z+4 a^3 z+2 a z-z a^{-1} -z a^{-3} +a^6+2 a^4+2 a^2+ a^{-2} +3 }[/math] |
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