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What you want to do is annotate the query, so that you get back your usual results but also have some data added to the result. So:
MyModel.objects.annotate(Min("value"))
Will return the normal result with mymodel__min
as an additional value
In reply to your comment, I think this is what you are looking for? This will return the dates with their corresponding Min values.
MyModel.objects.values('date').annotate(Min("value"))
Edit: In further reply to your comment in that you want the lowest valued entry but also want the additional date field within your result, you could do something like so:
MyModel.objects.values('date').annotate(min_value=Min('value')).order_by('min_value')[0]
This will get the resulting dict you are asking for by ordering the results and then simply taking the first index which will always be the lowest value.
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Source:stackexchange.com