K12a612
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+8 q^8-13 q^7+18 q^6-21 q^5+22 q^4-20 q^3+16 q^2-11 q+7-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+17 t^2-32 t+39-32 t^{-1} +17 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-7 z^4+1 }[/math] |
| Determinant | 145 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6 a^{-4} -z^6 a^{-6} -2 z^4 a^{-2} -6 z^4 a^{-4} -z^4 a^{-6} +z^4 a^{-8} +z^4-6 z^2 a^{-4} +3 z^2 a^{-6} +z^2 a^{-8} +2 z^2+ a^{-2} -3 a^{-4} +3 a^{-6} - a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +11 z^{10} a^{-4} +7 z^{10} a^{-6} +3 z^9 a^{-1} +z^9 a^{-3} +9 z^9 a^{-5} +11 z^9 a^{-7} -16 z^8 a^{-2} -42 z^8 a^{-4} -13 z^8 a^{-6} +12 z^8 a^{-8} +z^8-14 z^7 a^{-1} -31 z^7 a^{-3} -52 z^7 a^{-5} -24 z^7 a^{-7} +11 z^7 a^{-9} +16 z^6 a^{-2} +48 z^6 a^{-4} -19 z^6 a^{-8} +8 z^6 a^{-10} -5 z^6+20 z^5 a^{-1} +52 z^5 a^{-3} +67 z^5 a^{-5} +18 z^5 a^{-7} -13 z^5 a^{-9} +4 z^5 a^{-11} -2 z^4 a^{-2} -24 z^4 a^{-4} +6 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +8 z^4-11 z^3 a^{-1} -28 z^3 a^{-3} -32 z^3 a^{-5} -11 z^3 a^{-7} +2 z^3 a^{-9} -2 z^3 a^{-11} -z^2 a^{-2} +11 z^2 a^{-4} +7 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} -5 z^2+2 z a^{-1} +5 z a^{-3} +5 z a^{-5} +3 z a^{-7} +z a^{-9} - a^{-2} -3 a^{-4} -3 a^{-6} - a^{-8} +1 }[/math] |
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