K12a564
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-3 q^{10}+6 q^9-11 q^8+15 q^7-19 q^6+21 q^5-19 q^4+17 q^3-12 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t^2+34 t-51+34 t^{-1} -8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -8 z^4+2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -3 z^4 a^{-4} -3 z^4 a^{-6} -z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} +z^2+ a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +4 z^{10} a^{-6} +7 z^{10} a^{-8} +3 z^{10} a^{-10} +8 z^9 a^{-5} +11 z^9 a^{-7} +6 z^9 a^{-9} +3 z^9 a^{-11} +10 z^8 a^{-4} +3 z^8 a^{-6} -18 z^8 a^{-8} -10 z^8 a^{-10} +z^8 a^{-12} +9 z^7 a^{-3} -12 z^7 a^{-5} -44 z^7 a^{-7} -38 z^7 a^{-9} -15 z^7 a^{-11} +6 z^6 a^{-2} -17 z^6 a^{-4} -31 z^6 a^{-6} +z^6 a^{-8} +4 z^6 a^{-10} -5 z^6 a^{-12} +3 z^5 a^{-1} -13 z^5 a^{-3} +2 z^5 a^{-5} +52 z^5 a^{-7} +59 z^5 a^{-9} +25 z^5 a^{-11} -6 z^4 a^{-2} +11 z^4 a^{-4} +33 z^4 a^{-6} +17 z^4 a^{-8} +10 z^4 a^{-10} +8 z^4 a^{-12} +z^4-2 z^3 a^{-1} +9 z^3 a^{-3} -2 z^3 a^{-5} -35 z^3 a^{-7} -38 z^3 a^{-9} -16 z^3 a^{-11} +4 z^2 a^{-2} -3 z^2 a^{-4} -16 z^2 a^{-6} -9 z^2 a^{-8} -5 z^2 a^{-10} -4 z^2 a^{-12} -z^2+2 z a^{-5} +10 z a^{-7} +12 z a^{-9} +4 z a^{-11} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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