K12a1147
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+7 q^7-11 q^6+15 q^5-19 q^4+19 q^3-17 q^2+14 q-9+5 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-15 t^2+24 t-27+24 t^{-1} -15 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-13 z^4-5 z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -6 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-14 z^4 a^{-2} -8 z^4 a^{-4} +4 z^4 a^{-6} +5 z^4-14 z^2 a^{-2} -4 z^2 a^{-4} +5 z^2 a^{-6} +8 z^2-4 a^{-2} - a^{-4} +2 a^{-6} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10} a^{-6} +3 z^9 a^{-1} +z^9 a^{-3} +3 z^9 a^{-5} +5 z^9 a^{-7} -z^8 a^{-2} -13 z^8 a^{-4} -4 z^8 a^{-6} +5 z^8 a^{-8} +3 z^8+2 a z^7-7 z^7 a^{-1} -7 z^7 a^{-5} -13 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-6 z^6 a^{-2} +21 z^6 a^{-4} +2 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} -9 z^6-6 a z^5+8 z^5 a^{-1} -8 z^5 a^{-3} +14 z^5 a^{-7} -8 z^5 a^{-9} -4 a^2 z^4+18 z^4 a^{-2} -18 z^4 a^{-4} -5 z^4 a^{-6} +12 z^4 a^{-8} -3 z^4 a^{-10} +12 z^4+4 a z^3-5 z^3 a^{-1} +17 z^3 a^{-3} +11 z^3 a^{-5} -11 z^3 a^{-7} +4 z^3 a^{-9} +4 a^2 z^2-19 z^2 a^{-2} +11 z^2 a^{-4} +6 z^2 a^{-6} -6 z^2 a^{-8} +2 z^2 a^{-10} -12 z^2-2 z a^{-1} -7 z a^{-3} -3 z a^{-5} +2 z a^{-7} +4 a^{-2} - a^{-4} -2 a^{-6} +4 }[/math] |
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