K12a145
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-4 q^{14}+9 q^{13}-16 q^{12}+22 q^{11}-27 q^{10}+28 q^9-26 q^8+21 q^7-13 q^6+8 q^5-3 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-21 t^2+39 t-47+39 t^{-1} -21 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^6+15 z^4+9 z^2+1 }[/math] |
| Determinant | 179 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +3 z^6 a^{-8} +2 z^6 a^{-10} +3 z^4 a^{-6} +11 z^4 a^{-8} +4 z^4 a^{-10} -3 z^4 a^{-12} +2 z^2 a^{-6} +13 z^2 a^{-8} -z^2 a^{-10} -6 z^2 a^{-12} +z^2 a^{-14} +5 a^{-8} -3 a^{-10} -2 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +4 z^{10} a^{-10} +8 z^{10} a^{-12} +4 z^{10} a^{-14} +6 z^9 a^{-9} +13 z^9 a^{-11} +14 z^9 a^{-13} +7 z^9 a^{-15} +6 z^8 a^{-8} +z^8 a^{-10} -6 z^8 a^{-12} +6 z^8 a^{-14} +7 z^8 a^{-16} +3 z^7 a^{-7} -10 z^7 a^{-9} -34 z^7 a^{-11} -33 z^7 a^{-13} -8 z^7 a^{-15} +4 z^7 a^{-17} +z^6 a^{-6} -17 z^6 a^{-8} -16 z^6 a^{-10} -8 z^6 a^{-12} -25 z^6 a^{-14} -14 z^6 a^{-16} +z^6 a^{-18} -7 z^5 a^{-7} +2 z^5 a^{-9} +36 z^5 a^{-11} +31 z^5 a^{-13} -5 z^5 a^{-15} -9 z^5 a^{-17} -3 z^4 a^{-6} +21 z^4 a^{-8} +23 z^4 a^{-10} +8 z^4 a^{-12} +18 z^4 a^{-14} +7 z^4 a^{-16} -2 z^4 a^{-18} +3 z^3 a^{-7} +6 z^3 a^{-9} -15 z^3 a^{-11} -19 z^3 a^{-13} +5 z^3 a^{-15} +6 z^3 a^{-17} +2 z^2 a^{-6} -16 z^2 a^{-8} -13 z^2 a^{-10} +3 z^2 a^{-12} -4 z^2 a^{-14} -z^2 a^{-16} +z^2 a^{-18} -4 z a^{-9} +2 z a^{-11} +6 z a^{-13} -z a^{-15} -z a^{-17} +5 a^{-8} +3 a^{-10} -2 a^{-12} - a^{-14} }[/math] |
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