K12a626
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+13 q^7-24 q^6+35 q^5-44 q^4+47 q^3-43 q^2+36 q-24+13 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-34 t^2+61 t-73+61 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 | 291 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -3 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-3 z^4 a^{-2} -3 z^4 a^{-4} +2 z^4 a^{-6} +2 z^4-z^2 a^{-4} +z^2 a^{-6} +z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +12 z^{10} a^{-2} +25 z^{10} a^{-4} +13 z^{10} a^{-6} +16 z^9 a^{-1} +29 z^9 a^{-3} +30 z^9 a^{-5} +17 z^9 a^{-7} -31 z^8 a^{-4} -7 z^8 a^{-6} +12 z^8 a^{-8} +12 z^8+5 a z^7-24 z^7 a^{-1} -71 z^7 a^{-3} -78 z^7 a^{-5} -31 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-33 z^6 a^{-2} -9 z^6 a^{-4} -20 z^6 a^{-6} -21 z^6 a^{-8} +z^6 a^{-10} -21 z^6-7 a z^5+9 z^5 a^{-1} +48 z^5 a^{-3} +60 z^5 a^{-5} +21 z^5 a^{-7} -7 z^5 a^{-9} -a^2 z^4+25 z^4 a^{-2} +15 z^4 a^{-4} +18 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +14 z^4+3 a z^3-z^3 a^{-1} -16 z^3 a^{-3} -20 z^3 a^{-5} -6 z^3 a^{-7} +2 z^3 a^{-9} -4 z^2 a^{-2} -2 z^2 a^{-4} -3 z^2 a^{-6} -2 z^2 a^{-8} -3 z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} +z a^{-7} -2 a^{-2} - a^{-4} }[/math] |
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