On a conjecture of Deines

Mentzelos Melistas

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arXiv · 2604.07295

On a conjecture of Deines

Mentzelos Melistas

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Abstract

Two elliptic curves defined over $\mathbb{Q}$ 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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Mentzelos Melistas. 2026-04-08. On a conjecture of Deines. https://arxiv.org/abs/2604.07295

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