K12a973
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{15}-5 q^{14}+12 q^{13}-21 q^{12}+30 q^{11}-37 q^{10}+38 q^9-36 q^8+29 q^7-18 q^6+11 q^5-4 q^4+q^3 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 8 t^3-29 t^2+53 t-63+53 t^{-1} -29 t^{-2} +8 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 8 z^6+19 z^4+9 z^2+1 }[/math] |
| Determinant | 243 |
| 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} +14 z^4 a^{-8} +7 z^4 a^{-10} -4 z^4 a^{-12} +15 z^2 a^{-8} +z^2 a^{-10} -8 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} +19 z^{10} a^{-12} +9 z^{10} a^{-14} +13 z^9 a^{-9} +21 z^9 a^{-11} +21 z^9 a^{-13} +13 z^9 a^{-15} +10 z^8 a^{-8} -13 z^8 a^{-10} -34 z^8 a^{-12} +11 z^8 a^{-16} +4 z^7 a^{-7} -31 z^7 a^{-9} -70 z^7 a^{-11} -60 z^7 a^{-13} -20 z^7 a^{-15} +5 z^7 a^{-17} +z^6 a^{-6} -26 z^6 a^{-8} -4 z^6 a^{-10} +18 z^6 a^{-12} -27 z^6 a^{-14} -21 z^6 a^{-16} +z^6 a^{-18} -7 z^5 a^{-7} +26 z^5 a^{-9} +80 z^5 a^{-11} +59 z^5 a^{-13} +4 z^5 a^{-15} -8 z^5 a^{-17} -2 z^4 a^{-6} +26 z^4 a^{-8} +17 z^4 a^{-10} -4 z^4 a^{-12} +19 z^4 a^{-14} +11 z^4 a^{-16} -z^4 a^{-18} -2 z^3 a^{-9} -31 z^3 a^{-11} -32 z^3 a^{-13} +3 z^3 a^{-17} -15 z^2 a^{-8} -7 z^2 a^{-10} +6 z^2 a^{-12} -3 z^2 a^{-14} -z^2 a^{-16} -5 z a^{-9} +6 z a^{-13} +z a^{-15} +5 a^{-8} +3 a^{-10} -2 a^{-12} - a^{-14} }[/math] |
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