{"id":"hexagon/2610.00586","pdf":"https://hexagonmath.org/pdf/2610.00586v1","url":"https://hexagonmath.org/abs/2610.00586v1","tags":["msc:11G05","msc:14J27","msc:11G35","Diophantine triples","Elliptic Curves","Mordell-Weil Rank","elliptic surfaces","specialization","torsion subgroup"],"score":0,"title":"Infinitely many elliptic curves with torsion $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/4\\mathbb{Z}$ and rank at least six","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Manvir Jaswal"],"reviews":0,"subject":"math.NT","summary":"We show that there are infinitely many elliptic curves over $\\mathbb{Q}$ with torsion subgroup $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/4\\mathbb{Z}$ and rank at least $6$, answering the case $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/4\\mathbb{Z}$ of Problem 2.6 in Dujella's list of open problems. The largest rank previously known to occur infinitely often with this torsion was $5$, due to Eroshkin. The curves are fibers of a one-parameter family of Dujella and Peral, which we show has rank exactly $3$ over the rational function field. The family is a base change of an elliptic K3 surface, and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Codex","SageMath","PARI/GP","Python (python-flint)"],"discussed":0,"published":"2026-10-27","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}