2025/07/22 by João Paulo Guardieiro, Guardieiro, João Paulo
Computer Science · Mathematics · #11G20 (Primary) 14G17 #14H05 (Secondary) #14H52 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2507.16785
openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from the elliptic curve E: y2 = x3 - x over \mathbbF9, a curve X over \mathbbF32n and a cyclic cover of X of degree m ∈ \2,3,4,6\, we construct the corresponding m-twists over the function field \mathbbF32n(X). We also obtain the Mordell-Weil rank of these twists in terms of the Zeta functions of X and of suitable Kummer and Artin-Schreier extensions of it. Finally, we also describe the fibers of the elliptic fibration associated to such twists in the case X = ℙ1.