Your question is good because you are thinking of whether you need this table or not. That shows you care about the quality of your design.
The notation part has been fully answered by others, so I will focus more on the other part.
Should I show the table created supplier_product or leave it out and have the relationship many to many between supplier and product?
You need to find the answer not only from a technical perspective but also from a business perspective. For example, you need to ask a question like this:
Do I need to know when a supplier started supplying a product to the company?
Is the price of a supplied item depndent on the time or quantity supplied?
Is there a minimum quantity a supplier must supply per order that we need to know about?
Would there be associations between supplier_product to other classes in the model?
If your business has no interesting properties to place in the intersection table and there are no required associations (as in the above questions) and If you are doing the class diagram as part of high-level design from an OO perspective, you could do as @Kenvin Cline suggests and not include the class in your current version of the model.
If you want to be precise and clear and/or If you plan to implement the design at this stage in a relational database, either yourself or the application you'll use to create (forward engineer) the DLL will have to deal with the missing class representing the many-to-many relationship. Some tools could automatically create a Primary Key and FKs and RI constraints (of the tool's choice) and name all that in a way you may or may not accept. Also, your ORM mapper will have to create code to deal with this hidden table.
The effect of RI is critical and should always be checked and controlled. You need to precisely determine what happens to the supplied item information when a supplier is deleted from a database.
If you were doing a physical database design, then I would definitely suggest you flesh out your design and not let the tools do that for you unless you are entirely familiar with how and what the tools will build for you.