{"id":"hexagon/2610.00294","pdf":"https://hexagonmath.org/pdf/2610.00294v1","url":"https://hexagonmath.org/abs/2610.00294v1","tags":["math.AG","msc:11R45","msc:11G05","msc:14H52"],"score":0,"title":"Rational points on elliptic curves that are primitive modulo a positive proportion of primes","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Manjul Bhargava"],"reviews":0,"subject":"math.NT","summary":"In 1977, Lang and Trotter conjectured that, subject to certain necessary arithmetic restrictions, a rational point $P$ of infinite order on an elliptic curve $E$ over $\\Q$ should generate its reduction modulo infinitely many primes $p$---and indeed should do so for a specified positive density of primes. However, to date, even this infinitude was not known unconditionally for any explicit pair $(E,P)$. For the curve $E:y^2=x^3-2x$ and point $P=(2,2)$, we prove the existence of infinitely many---and indeed a positive lower density of---primes for which the reduction of $P$ generates…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}