The rule is that l' (elision) takes precedence over au (contraction).* The second pair will combine first if possible, in which case the first pair will not.
Hence, what's "hidden" by that apostrophe is not the a of la but the e of le !
The exact same goes for du vs. de l'. That is, de l'estomac, not du estomac.
However, it doesn't affect aux and des since the elision is not available for les, so the contraction wins. So aux estomacs, des estomacs.
* That would be analyzing it in terms of rule order. Another analysis would be that the article and the noun are more tightly bound than the article and the preposition, i.e. they form a smaller unit.
A third analysis would be to compare the outcomes at the word boundary: either two vowels /o ε/ (hiatus) or vowel-consonant-vowel /a lε/. LPH argues that French prefers the latter (consecutive vowels are the same thing addressed by liaison).