Isogenies of non-CM elliptic curves with rational j-invariants over\n number fields

2015/06/09 by Filip Najman, Najman, Filip
Arts and Humanities · Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1506.03127

openalex publication_date 2015/06/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We unconditionally determine I_ Q(d), the set of possible prime degrees of\ncyclic K-isogneies of elliptic curves with Q-rational j-invariants and\nwithout complex multiplication over number fields K of degree \≤ d, for\nd\≤ 7, and give an upper bound for I_ Q(d) for d>7. Assuming Serre's\nuniformity conjecture, we determine I_ Q(d) exactly for all positive integers\nd.\n

Citations

• The modular curves X0(65) and X0(91) and rational isogeny

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