K12n691
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-3 q^{14}+5 q^{13}-7 q^{12}+7 q^{11}-7 q^{10}+5 q^9-3 q^8+q^7+2 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-3 t^3-2 t^2+12 t-17+12 t^{-1} -2 t^{-2} -3 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+13 z^6+20 z^4+9 z^2+1 }[/math] |
| Determinant | 35 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +7 z^6 a^{-10} -z^6 a^{-12} +15 z^4 a^{-8} +13 z^4 a^{-10} -8 z^4 a^{-12} +13 z^2 a^{-8} +7 z^2 a^{-10} -13 z^2 a^{-12} +2 z^2 a^{-14} +4 a^{-8} -5 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +2 z^9 a^{-11} +2 z^9 a^{-13} +z^9 a^{-15} +z^8 a^{-8} -7 z^8 a^{-10} -7 z^8 a^{-12} +4 z^8 a^{-14} +3 z^8 a^{-16} -6 z^7 a^{-9} -16 z^7 a^{-11} -11 z^7 a^{-13} +2 z^7 a^{-15} +3 z^7 a^{-17} -7 z^6 a^{-8} +12 z^6 a^{-10} +15 z^6 a^{-12} -13 z^6 a^{-14} -8 z^6 a^{-16} +z^6 a^{-18} +7 z^5 a^{-9} +34 z^5 a^{-11} +23 z^5 a^{-13} -14 z^5 a^{-15} -10 z^5 a^{-17} +15 z^4 a^{-8} -5 z^4 a^{-10} -14 z^4 a^{-12} +11 z^4 a^{-14} +2 z^4 a^{-16} -3 z^4 a^{-18} +2 z^3 a^{-9} -20 z^3 a^{-11} -20 z^3 a^{-13} +10 z^3 a^{-15} +8 z^3 a^{-17} -13 z^2 a^{-8} +z^2 a^{-10} +14 z^2 a^{-12} -2 z^2 a^{-14} +2 z^2 a^{-18} -4 z a^{-9} +3 z a^{-11} +7 z a^{-13} -2 z a^{-15} -2 z a^{-17} +4 a^{-8} -5 a^{-12} -2 a^{-14} }[/math] |
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