K13a357
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Polynomial invariants
| Jones polynomial | Data:K13a357/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 11 t^3-48 t^2+101 t-127+101 t^{-1} -48 t^{-2} +11 t^{-3} }[/math] |
| Conway polynomial | Data:K13a357/Conway Polynomial |
| Determinant | 447 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} +5 z^6 a^{-8} +5 z^6 a^{-10} +z^4 a^{-6} +14 z^4 a^{-8} +12 z^4 a^{-10} -9 z^4 a^{-12} +13 z^2 a^{-8} +9 z^2 a^{-10} -19 z^2 a^{-12} +5 z^2 a^{-14} +4 a^{-8} +2 a^{-10} -10 a^{-12} +6 a^{-14} - a^{-16} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-12} +3 z^{12} a^{-14} +14 z^{11} a^{-11} +24 z^{11} a^{-13} +10 z^{11} a^{-15} +26 z^{10} a^{-10} +51 z^{10} a^{-12} +39 z^{10} a^{-14} +14 z^{10} a^{-16} +25 z^9 a^{-9} +24 z^9 a^{-11} +z^9 a^{-13} +13 z^9 a^{-15} +11 z^9 a^{-17} +15 z^8 a^{-8} -35 z^8 a^{-10} -124 z^8 a^{-12} -99 z^8 a^{-14} -20 z^8 a^{-16} +5 z^8 a^{-18} +5 z^7 a^{-7} -42 z^7 a^{-9} -112 z^7 a^{-11} -123 z^7 a^{-13} -84 z^7 a^{-15} -25 z^7 a^{-17} +z^7 a^{-19} +z^6 a^{-6} -24 z^6 a^{-8} +9 z^6 a^{-10} +96 z^6 a^{-12} +66 z^6 a^{-14} -8 z^6 a^{-16} -12 z^6 a^{-18} -4 z^5 a^{-7} +26 z^5 a^{-9} +121 z^5 a^{-11} +175 z^5 a^{-13} +107 z^5 a^{-15} +21 z^5 a^{-17} -2 z^5 a^{-19} -z^4 a^{-6} +21 z^4 a^{-8} -2 z^4 a^{-10} -44 z^4 a^{-12} -5 z^4 a^{-14} +25 z^4 a^{-16} +10 z^4 a^{-18} -4 z^3 a^{-9} -62 z^3 a^{-11} -110 z^3 a^{-13} -63 z^3 a^{-15} -10 z^3 a^{-17} +z^3 a^{-19} -13 z^2 a^{-8} +5 z^2 a^{-10} +26 z^2 a^{-12} -11 z^2 a^{-16} -3 z^2 a^{-18} -3 z a^{-9} +14 z a^{-11} +32 z a^{-13} +18 z a^{-15} +3 z a^{-17} +4 a^{-8} -2 a^{-10} -10 a^{-12} -6 a^{-14} - a^{-16} }[/math] |
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