K12a308
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+17 q^2-24 q+30-32 q^{-1} +29 q^{-2} -24 q^{-3} +17 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+16 t^2-48 t+69-48 t^{-1} +16 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+4 z^4-2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+2 z^4 a^4+z^2 a^4+a^4-z^6 a^2-z^2 a^2-a^2-z^6-z^2+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^8-8 a^4 z^8-21 a^2 z^8+11 z^8 a^{-2} +2 z^8+a^7 z^7-21 a^5 z^7-55 a^3 z^7-54 a z^7-13 z^7 a^{-1} +8 z^7 a^{-3} -13 a^6 z^6-16 a^4 z^6-10 a^2 z^6-14 z^6 a^{-2} +4 z^6 a^{-4} -25 z^6-3 a^7 z^5+19 a^5 z^5+60 a^3 z^5+54 a z^5+5 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4+28 a^4 z^4+29 a^2 z^4+6 z^4 a^{-2} -5 z^4 a^{-4} +25 z^4+2 a^7 z^3-8 a^5 z^3-30 a^3 z^3-28 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -5 a^6 z^2-13 a^4 z^2-14 a^2 z^2+2 z^2 a^{-4} -8 z^2+2 a^5 z+8 a^3 z+8 a z+2 z a^{-1} +a^4+a^2- a^{-2} }[/math] |
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