K12a753
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+3 q^2-5 q+8-10 q^{-1} +12 q^{-2} -12 q^{-3} +11 q^{-4} -9 q^{-5} +7 q^{-6} -4 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^2-21 t+31-21 t^{-1} +6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^4+3 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^8-a^8+z^4 a^6+z^2 a^6+a^6+2 z^4 a^4+2 z^2 a^4+2 z^4 a^2+2 z^2 a^2+a^2+z^4-z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^7 z^{11}+a^5 z^{11}+2 a^8 z^{10}+6 a^6 z^{10}+4 a^4 z^{10}+a^9 z^9-a^7 z^9+5 a^5 z^9+7 a^3 z^9-13 a^8 z^8-32 a^6 z^8-11 a^4 z^8+8 a^2 z^8-7 a^9 z^7-19 a^7 z^7-43 a^5 z^7-23 a^3 z^7+8 a z^7+29 a^8 z^6+53 a^6 z^6-3 a^4 z^6-20 a^2 z^6+7 z^6+17 a^9 z^5+54 a^7 z^5+76 a^5 z^5+19 a^3 z^5-15 a z^5+5 z^5 a^{-1} -27 a^8 z^4-32 a^6 z^4+15 a^4 z^4+8 a^2 z^4+3 z^4 a^{-2} -9 z^4-17 a^9 z^3-47 a^7 z^3-46 a^5 z^3-8 a^3 z^3+4 a z^3-3 z^3 a^{-1} +z^3 a^{-3} +10 a^8 z^2+8 a^6 z^2-4 a^4 z^2+a^2 z^2-z^2 a^{-2} +2 z^2+6 a^9 z+12 a^7 z+9 a^5 z+3 a^3 z-a^8-a^6-a^2 }[/math] |
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