K12a892
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+18 q^7-26 q^6+33 q^5-36 q^4+34 q^3-28 q^2+20 q-11+5 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+53 t-69+53 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 227 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +3 z^4 a^{-4} +z^4 a^{-6} -z^4 a^{-8} -z^4-z^2 a^{-2} +z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} - a^{-4} +2 a^{-6} - a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +12 z^{10} a^{-4} +21 z^{10} a^{-6} +9 z^{10} a^{-8} +17 z^9 a^{-3} +16 z^9 a^{-5} +7 z^9 a^{-7} +8 z^9 a^{-9} +16 z^8 a^{-2} -14 z^8 a^{-4} -59 z^8 a^{-6} -25 z^8 a^{-8} +4 z^8 a^{-10} +11 z^7 a^{-1} -28 z^7 a^{-3} -63 z^7 a^{-5} -50 z^7 a^{-7} -25 z^7 a^{-9} +z^7 a^{-11} -22 z^6 a^{-2} -4 z^6 a^{-4} +57 z^6 a^{-6} +22 z^6 a^{-8} -12 z^6 a^{-10} +5 z^6+a z^5-12 z^5 a^{-1} +16 z^5 a^{-3} +66 z^5 a^{-5} +65 z^5 a^{-7} +25 z^5 a^{-9} -3 z^5 a^{-11} +7 z^4 a^{-2} +8 z^4 a^{-4} -24 z^4 a^{-6} -12 z^4 a^{-8} +9 z^4 a^{-10} -4 z^4+z^3 a^{-1} -5 z^3 a^{-3} -22 z^3 a^{-5} -32 z^3 a^{-7} -14 z^3 a^{-9} +2 z^3 a^{-11} -2 z^2 a^{-2} +z^2 a^{-4} +9 z^2 a^{-6} +4 z^2 a^{-8} -2 z^2 a^{-10} +2 z a^{-5} +5 z a^{-7} +3 z a^{-9} - a^{-4} -2 a^{-6} - a^{-8} +1 }[/math] |
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