Nice elliptic curves

2023/06/15 by Van Huynh, Duc
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.08821

Abstract

In this work, we study elliptic curves of the form E_L: y² = x(x-1)(x-L), where L²-L+1 ∈ (ℚ^×)² and L ∈ ℚ ∖ \0,1\. We will show that for almost all quadratic extensions K/ℚ except one we have E_L(K) ≅ ℤ/2ℤ ⊕ ℤ/2ℤ.

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