Praise be to Allah.
The kind of love that is permissible is that which arises in a person's heart without there being any intention to do something haraam such as looking or mixing etc. As far as talking or writing to the girl is concerned, if this will lead to haraam actions or there is the fear that it may do so, then it is not permitted.
In general terms, we advise you not to do that, because it may start off innocently and in a proper manner, then develop in such a way that it makes a person do something haraam. If your parents do not want you to marry this girl, then try to convince them, and if you cannot, then look for someone else, because there may be something good in that although you may not realize it.