Replace Battery Inspiron 1545

Greetings,

I want to purchase a replacement battery for my Inspiron 1545 Laptop purchased new from DELL in Jan. of 2010.

The existing battery P/N = 0N586M (CN-0N586M-48630-9CK-04AI-A00)

The current recommended P/N from the DELL Support Website appears to be different (312-0844)

Can someone confirm if this is the correct P/N

Thanks Much
Scot