K12a809
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-11 q^9+18 q^8-26 q^7+30 q^6-31 q^5+29 q^4-22 q^3+15 q^2-8 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+27 t^2-39 t+43-39 t^{-1} +27 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +3 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +6 z^4 a^{-4} -2 z^4 a^{-8} -z^2 a^{-2} +7 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +4 a^{-4} -4 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +16 z^{10} a^{-6} +9 z^{10} a^{-8} +7 z^9 a^{-3} +6 z^9 a^{-5} +12 z^9 a^{-7} +13 z^9 a^{-9} +4 z^8 a^{-2} -19 z^8 a^{-4} -46 z^8 a^{-6} -9 z^8 a^{-8} +14 z^8 a^{-10} +z^7 a^{-1} -24 z^7 a^{-3} -44 z^7 a^{-5} -45 z^7 a^{-7} -15 z^7 a^{-9} +11 z^7 a^{-11} -14 z^6 a^{-2} +8 z^6 a^{-4} +44 z^6 a^{-6} -17 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +23 z^5 a^{-3} +60 z^5 a^{-5} +48 z^5 a^{-7} -z^5 a^{-9} -14 z^5 a^{-11} +z^5 a^{-13} +12 z^4 a^{-2} +12 z^4 a^{-4} -6 z^4 a^{-6} -2 z^4 a^{-8} -4 z^4 a^{-12} +z^3 a^{-1} -8 z^3 a^{-3} -24 z^3 a^{-5} -17 z^3 a^{-7} +z^3 a^{-9} +3 z^3 a^{-11} -3 z^2 a^{-2} -12 z^2 a^{-4} -11 z^2 a^{-6} +2 z^2 a^{-10} +z a^{-3} +2 z a^{-9} +z a^{-11} +4 a^{-4} +4 a^{-6} + a^{-8} }[/math] |
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