K12a127
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-15 q^6+21 q^5-24 q^4+25 q^3-23 q^2+17 q-11+6 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-17 t^2+37 t-45+37 t^{-1} -17 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+z^4-4 z^2+1 }[/math] |
| Determinant | 159 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +6 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-4 z^2 a^{-2} +8 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} -4 z^2+2 a^2-3 a^{-2} +5 a^{-4} -3 a^{-6} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +4 z^9 a^{-1} +9 z^9 a^{-3} +12 z^9 a^{-5} +7 z^9 a^{-7} -z^8 a^{-2} -7 z^8 a^{-4} +4 z^8 a^{-6} +7 z^8 a^{-8} +3 z^8+2 a z^7-9 z^7 a^{-1} -31 z^7 a^{-3} -34 z^7 a^{-5} -10 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-9 z^6 a^{-2} -16 z^6 a^{-4} -29 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -5 z^6-5 a z^5+14 z^5 a^{-1} +48 z^5 a^{-3} +34 z^5 a^{-5} -4 z^5 a^{-7} -9 z^5 a^{-9} -4 a^2 z^4+22 z^4 a^{-2} +43 z^4 a^{-4} +34 z^4 a^{-6} +8 z^4 a^{-8} -2 z^4 a^{-10} -z^4+2 a z^3-17 z^3 a^{-1} -31 z^3 a^{-3} -12 z^3 a^{-5} +5 z^3 a^{-7} +5 z^3 a^{-9} +5 a^2 z^2-18 z^2 a^{-2} -28 z^2 a^{-4} -17 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} +3 z^2+a z+7 z a^{-1} +8 z a^{-3} +2 z a^{-5} -z a^{-7} -z a^{-9} -2 a^2+3 a^{-2} +5 a^{-4} +3 a^{-6} + a^{-8} -1 }[/math] |
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