K13a133
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Polynomial invariants
| Jones polynomial | Data:K13a133/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-13 t^3+31 t^2-49 t+57-49 t^{-1} +31 t^{-2} -13 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | Data:K13a133/Conway Polynomial |
| Determinant | 249 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^8 a^{-2} +z^8-a^2 z^6+11 z^6 a^{-2} -3 z^6 a^{-4} +4 z^6-4 a^2 z^4+24 z^4 a^{-2} -13 z^4 a^{-4} +z^4 a^{-6} +5 z^4-5 a^2 z^2+26 z^2 a^{-2} -19 z^2 a^{-4} +3 z^2 a^{-6} +z^2-2 a^2+12 a^{-2} -10 a^{-4} +2 a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-2} +z^{12} a^{-4} +5 z^{11} a^{-1} +9 z^{11} a^{-3} +4 z^{11} a^{-5} +21 z^{10} a^{-2} +17 z^{10} a^{-4} +6 z^{10} a^{-6} +10 z^{10}+11 a z^9+11 z^9 a^{-1} -2 z^9 a^{-3} +2 z^9 a^{-5} +4 z^9 a^{-7} +9 a^2 z^8-70 z^8 a^{-2} -68 z^8 a^{-4} -20 z^8 a^{-6} +z^8 a^{-8} -14 z^8+6 a^3 z^7-18 a z^7-65 z^7 a^{-1} -78 z^7 a^{-3} -54 z^7 a^{-5} -17 z^7 a^{-7} +3 a^4 z^6-13 a^2 z^6+75 z^6 a^{-2} +77 z^6 a^{-4} +16 z^6 a^{-6} -4 z^6 a^{-8} +2 z^6+a^5 z^5-8 a^3 z^5+14 a z^5+93 z^5 a^{-1} +142 z^5 a^{-3} +97 z^5 a^{-5} +25 z^5 a^{-7} -4 a^4 z^4+11 a^2 z^4-47 z^4 a^{-2} -43 z^4 a^{-4} +5 z^4 a^{-8} +6 z^4-2 a^5 z^3+5 a^3 z^3-3 a z^3-62 z^3 a^{-1} -107 z^3 a^{-3} -71 z^3 a^{-5} -16 z^3 a^{-7} +a^4 z^2-6 a^2 z^2+28 z^2 a^{-2} +23 z^2 a^{-4} -2 z^2 a^{-8} +a^5 z-2 a^3 z+18 z a^{-1} +33 z a^{-3} +22 z a^{-5} +4 z a^{-7} +2 a^2-12 a^{-2} -10 a^{-4} -2 a^{-6} -1 }[/math] |
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