Reference describing supersingular elliptic curves over algebraically closed field in characteristic 2

Question

I'm looking for a reference for the fact that over an algebraically closed field of characteristic two, there is (essentially) only one supersingular elliptic curve.
This fact appears on Wikipedia, and there may be an exercise in a book of Silverman, but it would be great to cite a book or paper.
Thanks!

Ben Smith · Answer

This is stated and proven in Section 8.2 of
Max Deuring's Die Typen der Multiplikatorenringe elliptischer Funktionenkörper., Abh. Math. Semin. Hansische Univ. 14, 197-272 (1941). ZBL67.0107.01 (the case $p = 2$ starts at the bottom of Page 252).

Sarah Arpin · Answer

You could get it by brute force - the supersingular j-invariants have to lie in $mathbb{F}_{2^2}$, so you can just check each of them.

Reference describing supersingular elliptic curves over algebraically closed field in characteristic 2

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