Average rank in families of quadratic twists: a geometric point of view

2015/06/16 by Pierre Le Boudec, Boudec, Pierre Le
Mathematics · #11D45 #11G05 #14G05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D45 #msc:11G05 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1506.04980

arxiv created 2015/06/16 · arxiv updated 2015/06/17

Abstract

We investigate the average rank in the family of quadratic twists of a given elliptic curve defined over ℚ, when the curves are ordered using the canonical height of their lowest non-torsion rational point.

Related

• Average rank of quadratic twists with a rational point of almost minimal height
• The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields
• Rank frequencies for quadratic twists of elliptic curves
• Ranks of elliptic curves in families of quadratic twists
• The average analytic rank of elliptic curves