Some seed packets come with a few seeds to use as pollinators they are usually dyed different color to distinguish them from the others. That way you know which are which.

There are some new varieties that are only female and do not require a pollinator. I looked at the Burpee description and it doesn't mention the need for a separate pollinator. My guess is that you'll be fine with one plant. A way to be sure is to contact Burpee since it is their hybrid. Good luck!
Kim

Here is a link that might be useful: Kim's Garden

I think that's a gynoecious variety, no males needed. All the flowers won't set fruits, of course, but all will be potential fruit setters. When happy, the plants can be phenomenally productive.

I planted oriental express on a trellis this year. This is my first time growing these cucumbers. I was wondering the same thing about the pollination. My packet does say gynoecious type. And I planted them in a greenhouse. I have tons of cucumbers growing and WOW they are getting long!!! I did not do anything extra for polination.
My question is when should I pick them. They still look wrinkled and not smooth. are they supposed to be smooth when you pick them??

you don't want the fruit to be smooth. you want to have the bumps/ ribs. when totally smooth, the seed cavity is large and not as tasty.