K12a355
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-3 q^{14}+6 q^{13}-11 q^{12}+15 q^{11}-19 q^{10}+20 q^9-18 q^8+15 q^7-10 q^6+6 q^5-2 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-16 t^2+27 t-31+27 t^{-1} -16 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+14 z^4+8 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +2 z^6 a^{-8} +2 z^6 a^{-10} +4 z^4 a^{-6} +6 z^4 a^{-8} +7 z^4 a^{-10} -3 z^4 a^{-12} +5 z^2 a^{-6} +3 z^2 a^{-8} +8 z^2 a^{-10} -9 z^2 a^{-12} +z^2 a^{-14} +2 a^{-6} - a^{-8} +4 a^{-10} -6 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +7 z^{10} a^{-12} +4 z^{10} a^{-14} +3 z^9 a^{-9} +5 z^9 a^{-11} +8 z^9 a^{-13} +6 z^9 a^{-15} +3 z^8 a^{-8} -8 z^8 a^{-10} -25 z^8 a^{-12} -9 z^8 a^{-14} +5 z^8 a^{-16} +2 z^7 a^{-7} -4 z^7 a^{-9} -25 z^7 a^{-11} -42 z^7 a^{-13} -20 z^7 a^{-15} +3 z^7 a^{-17} +z^6 a^{-6} -6 z^6 a^{-8} +20 z^6 a^{-10} +46 z^6 a^{-12} +3 z^6 a^{-14} -15 z^6 a^{-16} +z^6 a^{-18} -5 z^5 a^{-7} +52 z^5 a^{-11} +80 z^5 a^{-13} +24 z^5 a^{-15} -9 z^5 a^{-17} -4 z^4 a^{-6} +z^4 a^{-8} -30 z^4 a^{-10} -41 z^4 a^{-12} +8 z^4 a^{-14} +11 z^4 a^{-16} -3 z^4 a^{-18} +2 z^3 a^{-7} -2 z^3 a^{-9} -45 z^3 a^{-11} -59 z^3 a^{-13} -13 z^3 a^{-15} +5 z^3 a^{-17} +5 z^2 a^{-6} +2 z^2 a^{-8} +17 z^2 a^{-10} +23 z^2 a^{-12} -z^2 a^{-14} -3 z^2 a^{-16} +z^2 a^{-18} +z a^{-7} +z a^{-9} +12 z a^{-11} +16 z a^{-13} +3 z a^{-15} -z a^{-17} -2 a^{-6} - a^{-8} -4 a^{-10} -6 a^{-12} -2 a^{-14} }[/math] |
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