K12a22
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+9 q^2-14 q+19-22 q^{-1} +23 q^{-2} -20 q^{-3} +16 q^{-4} -11 q^{-5} +6 q^{-6} -3 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-35 t+49-35 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4-z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-3 z^2 a^6-3 a^6+3 z^4 a^4+5 z^2 a^4+3 a^4-z^6 a^2-z^4 a^2-z^2 a^2-z^6-2 z^4-3 z^2-1+z^4 a^{-2} +z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+3 a^6 z^{10}+8 a^4 z^{10}+5 a^2 z^{10}+3 a^7 z^9+8 a^5 z^9+15 a^3 z^9+10 a z^9+a^8 z^8-9 a^6 z^8-20 a^4 z^8+3 a^2 z^8+13 z^8-15 a^7 z^7-49 a^5 z^7-59 a^3 z^7-12 a z^7+13 z^7 a^{-1} -5 a^8 z^6-2 a^6 z^6-5 a^4 z^6-34 a^2 z^6+9 z^6 a^{-2} -17 z^6+25 a^7 z^5+78 a^5 z^5+68 a^3 z^5-6 a z^5-17 z^5 a^{-1} +4 z^5 a^{-3} +8 a^8 z^4+22 a^6 z^4+35 a^4 z^4+30 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} -17 a^7 z^3-47 a^5 z^3-35 a^3 z^3+3 a z^3+7 z^3 a^{-1} -z^3 a^{-3} -5 a^8 z^2-16 a^6 z^2-20 a^4 z^2-8 a^2 z^2+3 z^2 a^{-2} +4 z^2+4 a^7 z+10 a^5 z+8 a^3 z+a z-z a^{-1} +a^8+3 a^6+3 a^4- a^{-2} -1 }[/math] |
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