K12a381
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-14 q^6+20 q^5-24 q^4+24 q^3-22 q^2+17 q-11+6 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-17 t^2+36 t-43+36 t^{-1} -17 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+z^4-5 z^2+1 }[/math] |
| Determinant | 155 |
| 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} +7 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} -4 z^2+2 a^2-2 a^{-2} +3 a^{-4} -2 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} +8 z^9 a^{-3} +11 z^9 a^{-5} +7 z^9 a^{-7} -2 z^8 a^{-2} -11 z^8 a^{-4} +z^8 a^{-6} +7 z^8 a^{-8} +3 z^8+2 a z^7-9 z^7 a^{-1} -27 z^7 a^{-3} -33 z^7 a^{-5} -13 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-4 z^6 a^{-2} +2 z^6 a^{-4} -17 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -5 z^6-5 a z^5+13 z^5 a^{-1} +41 z^5 a^{-3} +38 z^5 a^{-5} +6 z^5 a^{-7} -9 z^5 a^{-9} -4 a^2 z^4+12 z^4 a^{-2} +14 z^4 a^{-4} +16 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} -z^4+2 a z^3-14 z^3 a^{-1} -24 z^3 a^{-3} -17 z^3 a^{-5} -5 z^3 a^{-7} +4 z^3 a^{-9} +5 a^2 z^2-11 z^2 a^{-2} -11 z^2 a^{-4} -6 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} +3 z^2+a z+5 z a^{-1} +4 z a^{-3} +2 z a^{-5} +2 z a^{-7} -2 a^2+2 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} -1 }[/math] |
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