Étude expérimentale du rang de families de courbeselliptiques sur Q

DOI10.1080/10586458.1996.10504583zbMath0873.11033OpenAlexW2017819076MaRDI QIDQ4717343

Stéfane Fermigier

Publication date: 29 September 1997

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/233688

zbMATH Keywords

elliptic curvesBirch-Swinnerton-Dyer conjectureranks of the Mordell-Weil groupsShimura-Taniyama-Weil conjectureranks of the groups of rational points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Computational aspects of algebraic curves (14Q05)

Related Items (6)

From the Birch and Swinnerton-Dyer conjecture to Nagao’s conjecture ⋮ Average ranks of elliptic curves: Tension between data and conjecture ⋮ Effective equidistribution and the Sato-Tate law for families of elliptic curves ⋮ Some Results in the Theory of Low-Lying Zeros of Families of L-Functions ⋮ Uniform bounds on the number of rational points of a family of curves of genus 2 ⋮ Rational points on quadratic elliptic surfaces

Cites Work

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• Rank of elliptic curves and exponential sums
• An example of elliptic curve over \(\mathbb{Q}\) with rank \(\geq 20\)
• Average rank of families of elliptic curves and Sato-Tate laws
• Examples of elliptic curves over \(\mathbb{Q}\) with rank \(\geq 17\)
• Hecke operators on \(\Gamma_0(m)\)
• The behavior of the Mordell-Weil group of elliptic curves

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