Searching for 2001 Channel Balance
I believe the serial number is AO48316
Window size 31 1/8 x 46 1/4
This looks like a Series 775 Channel Balance. You'll need to measure the length of the metal channel to determine the length needed. You'll then need to select a stamp option & shoe size. Measure the size of the bottom shoe to know if you need a 1" or 1-1/4" shoe. For the stamp option, the one on your old balance looks a bit unusual. Obtain the exact weight of the window sash. You can then match that exact weight with one of the weight ranges listed alongside each stamp option on the balance shop page.
Shoe: 1.25"
Metal Channel: 20"
Sash weight: 12.5 lbs
Need 12 balances
Sounds like you need an S775-20 with a stamp option of 20B & the 1-1/4" Shoe. All orders can be placed right through that balance's shop page. Let me know if you have any further questions.