Tate-Shafarevich results for quartic twists in characteristic 2

2024/05/22 by Borges, Herivelto, Guardieiro, João Paulo, Salgado, Cecília +1 · 1 citation
#11G20 (Primary) #14G15 #14G17 #14H05 (Secondary) #14H52 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2405.13408

Abstract

The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study elliptic curves arising as quartic twist of a supersingular elliptic curve defined over \mathbbF₂ using the function field of a maximal curve C that admits an order 4 automorphism. For such elliptic curves we provide a rank formula for its Mordell-Weil group in terms of the genera of C and of another curve covered by C.

Cited by

• The ranks of twists of an elliptic curve in characteristic 3

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