Measured 27" long, 16/9" width, 5/8 deep, the mark is 2630

Based on your photos, you have either our S380-27 or S385-27. The only difference between them is the size of the bottom fitting, which is indicated on their respective store pages. You'll need to measure your bottom fitting to confirm which one is the better match.

Comparison of the S378, S380 and S385 balance shoes.