there is ,indeed, such a list and it is very short...over 2,000 years, the church has issued very few "infallible" statements...I'm sure Google will list them all for you....I won't.
What an odd reply regarding such a key tenet of your faith. You’d think a list of infallible, ex cathedra statements, rare and brief as you say, would be chiseled in stone somewhere amongst the statues and reliquaries. Or, might it be that there is no approved list of infallible, ex cathedra statements because papal infallibility only became doctrine in 1870?
I took your advice and Googled it, by the way. There is wide disagreement upon the matter, even on Catholic forums. Especially there, actually.