K12a431
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-5 q^{14}+13 q^{13}-24 q^{12}+34 q^{11}-42 q^{10}+44 q^9-41 q^8+33 q^7-21 q^6+12 q^5-4 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 8 t^3-31 t^2+61 t-75+61 t^{-1} -31 t^{-2} +8 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^6+17 z^4+9 z^2+1 }[/math] |
| Determinant | 275 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +4 z^6 a^{-8} +3 z^6 a^{-10} +2 z^4 a^{-6} +13 z^4 a^{-8} +6 z^4 a^{-10} -4 z^4 a^{-12} +z^2 a^{-6} +14 z^2 a^{-8} -7 z^2 a^{-12} +z^2 a^{-14} +5 a^{-8} -3 a^{-10} -2 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-11} +3 z^{11} a^{-13} +10 z^{10} a^{-10} +21 z^{10} a^{-12} +11 z^{10} a^{-14} +13 z^9 a^{-9} +29 z^9 a^{-11} +32 z^9 a^{-13} +16 z^9 a^{-15} +10 z^8 a^{-8} -19 z^8 a^{-12} +3 z^8 a^{-14} +12 z^8 a^{-16} +4 z^7 a^{-7} -20 z^7 a^{-9} -74 z^7 a^{-11} -81 z^7 a^{-13} -26 z^7 a^{-15} +5 z^7 a^{-17} +z^6 a^{-6} -21 z^6 a^{-8} -28 z^6 a^{-10} -24 z^6 a^{-12} -40 z^6 a^{-14} -21 z^6 a^{-16} +z^6 a^{-18} -6 z^5 a^{-7} +8 z^5 a^{-9} +62 z^5 a^{-11} +68 z^5 a^{-13} +13 z^5 a^{-15} -7 z^5 a^{-17} -2 z^4 a^{-6} +23 z^4 a^{-8} +29 z^4 a^{-10} +22 z^4 a^{-12} +32 z^4 a^{-14} +13 z^4 a^{-16} -z^4 a^{-18} +2 z^3 a^{-7} +5 z^3 a^{-9} -23 z^3 a^{-11} -34 z^3 a^{-13} -5 z^3 a^{-15} +3 z^3 a^{-17} +z^2 a^{-6} -16 z^2 a^{-8} -12 z^2 a^{-10} +z^2 a^{-12} -7 z^2 a^{-14} -3 z^2 a^{-16} -4 z a^{-9} +3 z a^{-11} +9 z a^{-13} +2 z a^{-15} +5 a^{-8} +3 a^{-10} -2 a^{-12} - a^{-14} }[/math] |
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