On the squareness of the discriminant of elliptic curves with an isogeny

2026/02/01 by Enrique González-Jiménez · 1 voice
Mathematics · #math.NT #math.AG

paper · pdf · doi:10.1007/s13398-025-01811-3

Abstract

We establish a classification of the values of \( N \) for which an elliptic curve defined over \( ℚ \) with square discriminant admits an \( N \)-isogeny. Furthermore, we determine the values of \( N \) for which two elliptic curves defined over \( ℚ \), both possessing square discriminants, are \( N \)-isogenous. In both cases, we explicitly parametrize the corresponding \( j \)-invariants of the elliptic curves associated with these problems.

Citations

• A classification of isogeny-torsion graphs of ℚ-isogeny classes of elliptic curves
• Composite images of Galois for elliptic curves over Q & Entanglement fields
• On the possible images of the mod ell representations associated to elliptic curves over Q
• Elliptic curves over ℚ and 2-adic images of Galois
• Galois Theory, discriminants and torsion subgroups of elliptic curves
• The Arithmetic of Elliptic Curves

Discussions

• On the squareness of the discriminant of elliptic curves with an isogeny - By arXiv https://arxiv.org/abs/2602.01384 Mathematics, Elliptic Curves, Isogenies, Discriminants, Algebraic Geometry [bsky, 0 points, 0 comments]

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