K12a922
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+11 q^7-22 q^6+33 q^5-42 q^4+46 q^3-43 q^2+36 q-25+14 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-32 t^2+60 t-73+60 t^{-1} -32 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-6 z^4-z^2+1 }[/math] |
| Determinant | 283 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -3 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-3 z^4 a^{-2} -8 z^4 a^{-4} +3 z^4 a^{-6} +2 z^4-7 z^2 a^{-4} +4 z^2 a^{-6} +2 z^2+ a^{-2} -2 a^{-4} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +13 z^{10} a^{-2} +24 z^{10} a^{-4} +11 z^{10} a^{-6} +18 z^9 a^{-1} +29 z^9 a^{-3} +24 z^9 a^{-5} +13 z^9 a^{-7} -3 z^8 a^{-2} -31 z^8 a^{-4} -6 z^8 a^{-6} +9 z^8 a^{-8} +13 z^8+5 a z^7-31 z^7 a^{-1} -72 z^7 a^{-3} -62 z^7 a^{-5} -22 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-32 z^6 a^{-2} -5 z^6 a^{-4} -14 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -23 z^6-6 a z^5+17 z^5 a^{-1} +47 z^5 a^{-3} +48 z^5 a^{-5} +17 z^5 a^{-7} -7 z^5 a^{-9} -a^2 z^4+25 z^4 a^{-2} +9 z^4 a^{-4} +15 z^4 a^{-6} +12 z^4 a^{-8} -2 z^4 a^{-10} +16 z^4+2 a z^3-6 z^3 a^{-1} -14 z^3 a^{-3} -16 z^3 a^{-5} -6 z^3 a^{-7} +4 z^3 a^{-9} -5 z^2 a^{-2} +4 z^2 a^{-4} -2 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} -6 z^2+z a^{-1} +3 z a^{-3} +3 z a^{-5} -z a^{-9} - a^{-2} -2 a^{-4} - a^{-6} +1 }[/math] |
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