What is the simplest example (or perhaps best reference) for the fact that there are genus 1 curves (over a field of your choice — or if you wish, over Q, to make it more exciting) with no points of degree less than n? Brian Conrad gave a slick answer here: https://math216.wordpress.com/2011/04/22/fourteenth-post/ but I wonder if there is something that can be explained more simply. My expectation is that this isn’t possible, because describing genus one curves extrinsically is hard, but there may be a clever trick I am missing.