K12a409
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+8 q^{11}-13 q^{10}+18 q^9-22 q^8+22 q^7-20 q^6+17 q^5-11 q^4+7 q^3-3 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-20 t^2+27 t-29+27 t^{-1} -20 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6+5 z^2+1 }[/math] |
| Determinant | 147 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -4 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} +4 z^4 a^{-4} -3 z^4 a^{-6} -4 z^4 a^{-8} +3 z^4 a^{-10} +4 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} + a^{-4} +2 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +4 z^{10} a^{-6} +11 z^{10} a^{-8} +7 z^{10} a^{-10} +3 z^9 a^{-5} +z^9 a^{-7} +9 z^9 a^{-9} +11 z^9 a^{-11} +z^8 a^{-4} -16 z^8 a^{-6} -41 z^8 a^{-8} -12 z^8 a^{-10} +12 z^8 a^{-12} -14 z^7 a^{-5} -30 z^7 a^{-7} -49 z^7 a^{-9} -22 z^7 a^{-11} +11 z^7 a^{-13} -5 z^6 a^{-4} +17 z^6 a^{-6} +45 z^6 a^{-8} -3 z^6 a^{-10} -18 z^6 a^{-12} +8 z^6 a^{-14} +20 z^5 a^{-5} +50 z^5 a^{-7} +57 z^5 a^{-9} +10 z^5 a^{-11} -13 z^5 a^{-13} +4 z^5 a^{-15} +8 z^4 a^{-4} -5 z^4 a^{-6} -20 z^4 a^{-8} +5 z^4 a^{-10} +4 z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -10 z^3 a^{-5} -28 z^3 a^{-7} -23 z^3 a^{-9} +3 z^3 a^{-13} -2 z^3 a^{-15} -5 z^2 a^{-4} +2 z^2 a^{-6} +7 z^2 a^{-8} +z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +6 z a^{-7} +4 z a^{-9} -z a^{-11} + a^{-4} -2 a^{-6} -2 a^{-8} }[/math] |
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