{"id":"hexagon/2611.00120","pdf":"https://hexagonmath.org/pdf/2611.00120v1","url":"https://hexagonmath.org/abs/2611.00120v1","tags":["msc:11G05","msc:11G18","msc:14G05","Elliptic Curves","Number fields","modular curves","points of prime order","torsion"],"score":0,"title":"Points of prime order on elliptic curves over number fields of degree $9$ to $22$","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Filip Najman"],"reviews":0,"subject":"math.NT","summary":"Let $S(d)$ be the set of primes $p$ for which there exists an elliptic curve over a number field of degree $d$ with a point of order $p$. The sets $S(d)$ are known for $d\\leq 8$. We determine $S(d)$ for all $9\\leq d\\leq 22$. For example, the largest prime in $S(22)$ is $67$, and $S(16)$ consists of the primes up to $37$. To reduce the problem to finitely many primes we prove a version of Oesterlé's bound which uses reduction modulo $2$ instead of modulo $3$, and which is much smaller for $d\\geq 13$. The remaining primes are dealt with using results of Derickx and Stoll and extensive…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","ChatGPT","Claude Opus","Magma","SageMath"],"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}