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On a conjecture of Deines | Synapse

April 13, 2026Open Access

On a conjecture of Deines

Puntos clave

The aim is to establish the existence of infinitely many semi-stable non-isogenous discriminant twins as conjectured by Deines.
Construct an explicit infinite family of elliptic curves
Analyze properties of their discriminants and conductors
Demonstrate that these curves are semi-stable and non-isogenous
Provided an explicit infinite family of semi-stable non-isogenous discriminant twins
Confirmed Deines' conjecture through constructed examples

Resumen

Two elliptic curves defined over Q are called discriminant twins if they have the same minimal discriminant and the same conductor. Deines, in 2014, conjectured that there exist infinitely many semi-stable non-isogenous discriminant twins. In this article we present an explicit infinite family of semi-stable non-isogenous discriminant twins, providing a proof for Deines' conjecture.

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Cite This Study

Mentzelos Melistas (Wed,) studied this question.

synapsesocial.com/papers/69dc874a3afacbeac03e9b6e https://doi.org/https://doi.org/10.48550/arxiv.2604.07295

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