K12a38
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-3 q^{10}+4 q^9-6 q^8+8 q^7-9 q^6+10 q^5-9 q^4+8 q^3-6 q^2+4 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^2+18 t-27+18 t^{-1} -4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^4+2 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -z^4 a^{-4} -z^4 a^{-6} -z^4 a^{-8} -z^2 a^{-2} +z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} +z^2- a^{-2} + a^{-4} + a^{-6} - a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} -z^9 a^{-7} +3 z^9 a^{-11} +2 z^8 a^{-4} -7 z^8 a^{-6} -26 z^8 a^{-8} -16 z^8 a^{-10} +z^8 a^{-12} +2 z^7 a^{-3} -4 z^7 a^{-5} -9 z^7 a^{-7} -20 z^7 a^{-9} -17 z^7 a^{-11} +2 z^6 a^{-2} -2 z^6 a^{-4} +11 z^6 a^{-6} +45 z^6 a^{-8} +25 z^6 a^{-10} -5 z^6 a^{-12} +2 z^5 a^{-1} +3 z^5 a^{-5} +19 z^5 a^{-7} +42 z^5 a^{-9} +28 z^5 a^{-11} +2 z^4 a^{-4} -13 z^4 a^{-6} -36 z^4 a^{-8} -14 z^4 a^{-10} +6 z^4 a^{-12} +z^4-3 z^3 a^{-1} -2 z^3 a^{-3} -z^3 a^{-5} -16 z^3 a^{-7} -28 z^3 a^{-9} -14 z^3 a^{-11} -3 z^2 a^{-2} -2 z^2 a^{-4} +7 z^2 a^{-6} +12 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-12} -2 z^2+z a^{-1} +z a^{-3} +4 z a^{-7} +5 z a^{-9} +z a^{-11} + a^{-2} + a^{-4} - a^{-6} - a^{-8} +1 }[/math] |
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