K12a659
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-5 q^{14}+12 q^{13}-22 q^{12}+32 q^{11}-40 q^{10}+42 q^9-39 q^8+32 q^7-21 q^6+12 q^5-4 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 8 t^3-30 t^2+58 t-71+58 t^{-1} -30 t^{-2} +8 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^6+18 z^4+10 z^2+1 }[/math] |
| Determinant | 263 |
| 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} +7 z^4 a^{-10} -4 z^4 a^{-12} +z^2 a^{-6} +13 z^2 a^{-8} +3 z^2 a^{-10} -8 z^2 a^{-12} +z^2 a^{-14} +4 a^{-8} - a^{-10} -3 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-11} +3 z^{11} a^{-13} +10 z^{10} a^{-10} +20 z^{10} a^{-12} +10 z^{10} a^{-14} +13 z^9 a^{-9} +26 z^9 a^{-11} +27 z^9 a^{-13} +14 z^9 a^{-15} +10 z^8 a^{-8} -3 z^8 a^{-10} -23 z^8 a^{-12} +z^8 a^{-14} +11 z^8 a^{-16} +4 z^7 a^{-7} -21 z^7 a^{-9} -69 z^7 a^{-11} -71 z^7 a^{-13} -22 z^7 a^{-15} +5 z^7 a^{-17} +z^6 a^{-6} -21 z^6 a^{-8} -21 z^6 a^{-10} -12 z^6 a^{-12} -34 z^6 a^{-14} -20 z^6 a^{-16} +z^6 a^{-18} -6 z^5 a^{-7} +9 z^5 a^{-9} +60 z^5 a^{-11} +60 z^5 a^{-13} +7 z^5 a^{-15} -8 z^5 a^{-17} -2 z^4 a^{-6} +22 z^4 a^{-8} +20 z^4 a^{-10} +15 z^4 a^{-12} +31 z^4 a^{-14} +11 z^4 a^{-16} -z^4 a^{-18} +2 z^3 a^{-7} +2 z^3 a^{-9} -23 z^3 a^{-11} -24 z^3 a^{-13} +2 z^3 a^{-15} +3 z^3 a^{-17} +z^2 a^{-6} -15 z^2 a^{-8} -7 z^2 a^{-10} +4 z^2 a^{-12} -7 z^2 a^{-14} -2 z^2 a^{-16} -3 z a^{-9} +3 z a^{-11} +5 z a^{-13} -z a^{-15} +4 a^{-8} + a^{-10} -3 a^{-12} - a^{-14} }[/math] |
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