K12a398
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-16 q^7+22 q^6-27 q^5+29 q^4-26 q^3+22 q^2-15 q+9-4 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-39 t+47-39 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -7 z^4 a^{-2} +12 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-8 z^2 a^{-2} +15 z^2 a^{-4} -9 z^2 a^{-6} +2 z^2 a^{-8} +2 z^2-3 a^{-2} +7 a^{-4} -5 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +13 z^{10} a^{-4} +8 z^{10} a^{-6} +4 z^9 a^{-1} +9 z^9 a^{-3} +20 z^9 a^{-5} +15 z^9 a^{-7} -15 z^8 a^{-2} -30 z^8 a^{-4} +4 z^8 a^{-6} +18 z^8 a^{-8} +z^8-17 z^7 a^{-1} -56 z^7 a^{-3} -75 z^7 a^{-5} -21 z^7 a^{-7} +15 z^7 a^{-9} +3 z^6 a^{-2} -13 z^6 a^{-4} -60 z^6 a^{-6} -31 z^6 a^{-8} +9 z^6 a^{-10} -4 z^6+24 z^5 a^{-1} +73 z^5 a^{-3} +62 z^5 a^{-5} -11 z^5 a^{-7} -20 z^5 a^{-9} +4 z^5 a^{-11} +22 z^4 a^{-2} +57 z^4 a^{-4} +65 z^4 a^{-6} +17 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +6 z^4-12 z^3 a^{-1} -27 z^3 a^{-3} -7 z^3 a^{-5} +19 z^3 a^{-7} +10 z^3 a^{-9} -z^3 a^{-11} -17 z^2 a^{-2} -33 z^2 a^{-4} -27 z^2 a^{-6} -6 z^2 a^{-8} +z^2 a^{-10} -4 z^2+z a^{-1} +z a^{-3} -5 z a^{-5} -7 z a^{-7} -2 z a^{-9} +3 a^{-2} +7 a^{-4} +5 a^{-6} + a^{-8} +1 }[/math] |
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