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arXiv · 2602.01384

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

Enrique González-Jiménez
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Abstract

We establish a classification of the values of \( N \) for which an elliptic curve defined over \( \mathbb{Q} \) with square discriminant admits an \( N \)-isogeny. Furthermore, we determine the values of \( N \) for which two elliptic curves defined over \( \mathbb{Q} \), 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.

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Enrique González-Jiménez. 2026-02-01. On the squareness of the discriminant of elliptic curves with an isogeny. https://doi.org/10.1007/s13398-025-01811-3

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