K12a816
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-8 q^3+14 q^2-19 q+23-23 q^{-1} +22 q^{-2} -16 q^{-3} +11 q^{-4} -6 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+17 t^2-30 t+37-30 t^{-1} +17 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+15 z^4+7 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+6 a^2 z^6-z^6 a^{-2} +5 z^6-5 a^4 z^4+15 a^2 z^4-4 z^4 a^{-2} +9 z^4-9 a^4 z^2+17 a^2 z^2-6 z^2 a^{-2} +5 z^2-5 a^4+8 a^2-2 a^{-2} }[/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}+3 a^5 z^9+6 a^3 z^9+10 a z^9+7 z^9 a^{-1} +2 a^6 z^8-8 a^4 z^8-17 a^2 z^8+8 z^8 a^{-2} +z^8+a^7 z^7-9 a^5 z^7-26 a^3 z^7-30 a z^7-8 z^7 a^{-1} +6 z^7 a^{-3} -7 a^6 z^6+13 a^4 z^6+26 a^2 z^6-13 z^6 a^{-2} +3 z^6 a^{-4} -10 z^6-5 a^7 z^5+8 a^5 z^5+43 a^3 z^5+42 a z^5+2 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} +6 a^6 z^4-23 a^4 z^4-35 a^2 z^4+12 z^4 a^{-2} -4 z^4 a^{-4} +10 z^4+8 a^7 z^3-4 a^5 z^3-42 a^3 z^3-35 a z^3+3 z^3 a^{-1} +6 z^3 a^{-3} -2 z^3 a^{-5} +19 a^4 z^2+24 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} -3 z^2-4 a^7 z+2 a^5 z+15 a^3 z+11 a z-z a^{-1} -2 z a^{-3} +z a^{-5} -5 a^4-8 a^2+2 a^{-2} }[/math] |
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