K12a557
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-3 q^{10}+6 q^9-10 q^8+13 q^7-15 q^6+16 q^5-15 q^4+12 q^3-8 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -7 t^2+27 t-39+27 t^{-1} -7 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -7 z^4-z^2+1 }[/math] |
| Determinant | 107 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -2 z^4 a^{-4} -3 z^4 a^{-6} -z^4 a^{-8} -4 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} +z^2+ a^{-4} -2 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +5 z^9 a^{-5} +6 z^9 a^{-7} +4 z^9 a^{-9} +3 z^9 a^{-11} +5 z^8 a^{-4} -z^8 a^{-6} -18 z^8 a^{-8} -11 z^8 a^{-10} +z^8 a^{-12} +4 z^7 a^{-3} -11 z^7 a^{-5} -30 z^7 a^{-7} -30 z^7 a^{-9} -15 z^7 a^{-11} +3 z^6 a^{-2} -9 z^6 a^{-4} -20 z^6 a^{-6} +4 z^6 a^{-8} +7 z^6 a^{-10} -5 z^6 a^{-12} +2 z^5 a^{-1} -4 z^5 a^{-3} +8 z^5 a^{-5} +31 z^5 a^{-7} +41 z^5 a^{-9} +24 z^5 a^{-11} -2 z^4 a^{-2} +8 z^4 a^{-4} +28 z^4 a^{-6} +14 z^4 a^{-8} +5 z^4 a^{-10} +8 z^4 a^{-12} +z^4-2 z^3 a^{-1} +2 z^3 a^{-3} -3 z^3 a^{-5} -11 z^3 a^{-7} -18 z^3 a^{-9} -14 z^3 a^{-11} -4 z^2 a^{-4} -14 z^2 a^{-6} -7 z^2 a^{-8} -3 z^2 a^{-10} -4 z^2 a^{-12} -2 z^2+z a^{-7} +3 z a^{-9} +2 z a^{-11} + a^{-4} +2 a^{-6} + a^{-8} +1 }[/math] |
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