K12a986
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-13 q^3+24 q^2-35 q+43-45 q^{-1} +43 q^{-2} -34 q^{-3} +23 q^{-4} -13 q^{-5} +5 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+34 t^2-59 t+71-59 t^{-1} +34 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+4 z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 285 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+3 a^2 z^6-z^6 a^{-2} +3 z^6-2 a^4 z^4+3 a^2 z^4-2 z^4 a^{-2} +3 z^4-a^4 z^2+2 a^2 z^2-z^2 a^{-2} +z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^3 z^{11}+5 a z^{11}+12 a^4 z^{10}+28 a^2 z^{10}+16 z^{10}+11 a^5 z^9+17 a^3 z^9+30 a z^9+24 z^9 a^{-1} +5 a^6 z^8-24 a^4 z^8-56 a^2 z^8+22 z^8 a^{-2} -5 z^8+a^7 z^7-29 a^5 z^7-70 a^3 z^7-87 a z^7-34 z^7 a^{-1} +13 z^7 a^{-3} -12 a^6 z^6+8 a^4 z^6+22 a^2 z^6-31 z^6 a^{-2} +5 z^6 a^{-4} -34 z^6-2 a^7 z^5+24 a^5 z^5+64 a^3 z^5+64 a z^5+13 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +8 a^6 z^4+3 a^4 z^4+a^2 z^4+17 z^4 a^{-2} -2 z^4 a^{-4} +25 z^4+a^7 z^3-7 a^5 z^3-22 a^3 z^3-20 a z^3-2 z^3 a^{-1} +4 z^3 a^{-3} -a^6 z^2+a^4 z^2+a^2 z^2-3 z^2 a^{-2} -4 z^2+2 a^5 z+4 a^3 z+3 a z+z a^{-1} -a^4-2 a^2 }[/math] |
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