To answer the question, this is how you would fit this in julia:
julia> using LsqFit
julia> d = [17,19,20,21,22,24,25,26];
julia> C = [41,62,201,291,440,830,1287,1975];
julia> model(x,p) = @. p/(1+exp(p*(p-x)));
julia> fit = curve_fit(model,d,C,[10000,0.5,10]);
julia> confidence_interval(fit, 0.05)
Interestingly we get a different value for L, not sure why. However, as expected, the confidence interval is huge, showing that this parameter is not important to the fit.
Note that LsqFit currently returns symmetric confidence intervals, which is why the lower bound makes no sense here.