How to treat a pumpkin plant ?

For the first time I have planted a pumpkin. It grew to gigantic proportions.
The plant has spread itself with branches of about 6 m all around.
Until now it's having only one huge pumpkin and two little ones. When I see the plant growing in others gardens, I noticed that one plant can have many pumpkins, and taking much less space.
Although mine gives an abundance of flowers, they don't grow into pumpkins (except of the three mentioned). The plant is looking very healthy.
Does anybody knows if I have to give it a special treatment in order to have more but smaller pumpkins ?

A lot depends on the variety of pumpkin. Some have more compact vines and others sprawl. Same with the pumpkins themselves...some have many fruits, others have just a few. There are many kinds of pumpkins.

If your plant is healthy, then chances are, you've got one of the varieties that do not produce as many.

One other thing I noticed from your picture...your pumpkin is in the shade. If you are not getting a full day of sunshine, then production could suffer. Pumpkins need full sun all day to produce their best.

Thanks so much Melody, for your response.
Unfortunately the tag on the plant I bought in a garden centre only mentioned 'Pumpkin' without any other specification.

You are right in noticing that my pumpkin doesn't has full sun the whole day, but it still gets a lot. The picture was taken in the evening which explains the shadows on the pumpkin.