K12a615
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-6 q^{14}+14 q^{13}-23 q^{12}+32 q^{11}-38 q^{10}+38 q^9-35 q^8+27 q^7-16 q^6+9 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 7 t^3-27 t^2+54 t-67+54 t^{-1} -27 t^{-2} +7 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 7 z^6+15 z^4+9 z^2+1 }[/math] |
| Determinant | 243 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +3 z^6 a^{-10} +3 z^4 a^{-6} +9 z^4 a^{-8} +7 z^4 a^{-10} -4 z^4 a^{-12} +3 z^2 a^{-6} +9 z^2 a^{-8} +2 z^2 a^{-10} -6 z^2 a^{-12} +z^2 a^{-14} + a^{-6} +3 a^{-8} -3 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-11} +2 z^{11} a^{-13} +6 z^{10} a^{-10} +15 z^{10} a^{-12} +9 z^{10} a^{-14} +7 z^9 a^{-9} +20 z^9 a^{-11} +29 z^9 a^{-13} +16 z^9 a^{-15} +6 z^8 a^{-8} +2 z^8 a^{-10} -8 z^8 a^{-12} +10 z^8 a^{-14} +14 z^8 a^{-16} +3 z^7 a^{-7} -6 z^7 a^{-9} -48 z^7 a^{-11} -69 z^7 a^{-13} -24 z^7 a^{-15} +6 z^7 a^{-17} +z^6 a^{-6} -12 z^6 a^{-8} -18 z^6 a^{-10} -34 z^6 a^{-12} -55 z^6 a^{-14} -25 z^6 a^{-16} +z^6 a^{-18} -6 z^5 a^{-7} -6 z^5 a^{-9} +38 z^5 a^{-11} +46 z^5 a^{-13} +z^5 a^{-15} -7 z^5 a^{-17} -3 z^4 a^{-6} +12 z^4 a^{-8} +21 z^4 a^{-10} +37 z^4 a^{-12} +40 z^4 a^{-14} +9 z^4 a^{-16} +3 z^3 a^{-7} +12 z^3 a^{-9} -3 z^3 a^{-11} -9 z^3 a^{-13} +3 z^3 a^{-15} +3 z^2 a^{-6} -9 z^2 a^{-8} -10 z^2 a^{-10} -6 z^2 a^{-12} -7 z^2 a^{-14} +z^2 a^{-16} -6 z a^{-9} -6 z a^{-11} -2 z a^{-13} -z a^{-15} +z a^{-17} - a^{-6} +3 a^{-8} +3 a^{-10} }[/math] |
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