On the rank of elliptic curves
General Mathematics
2020-07-08 v2
Authors:
Jorma Jormakka
Abstract
The paper proves that the Birch and Swinnerton-Dyer conjecture is false.
Cite
@article{arxiv.0809.4091,
title = {On the rank of elliptic curves},
author = {Jorma Jormakka},
journal= {arXiv preprint arXiv:0809.4091},
year = {2020}
}
Comments
48 pages
Related papers
View all related →
Number Theory · Mathematics
A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture
Manjul Bhargava, Christopher Skinner, Wei Zhang
2014-07-18
Number Theory · Mathematics
The 2-parity conjecture for elliptic curves with isomorphic 2-torsion
Holly Green, Celine Maistret
2022-10-12
Number Theory · Mathematics
The Birch and Swinnerton-Dyer conjecture for an elliptic curve over $\mathbb{Q}(\sqrt[4]{5})$
Raymond van Bommel
2018-06-20
Number Theory · Mathematics
Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves
Jie Shu, Shuai Zhai
2021-02-24
Number Theory · Mathematics
On the 2-part of the Birch and Swinnerton-Dyer conjecture for quadratic twists of elliptic curves
Li Cai, Chao Li, Shuai Zhai
2019-11-14
Number Theory · Mathematics
On the parity of ranks of Selmer groups II
Jan Nekovar
2009-11-07
Number Theory · Mathematics
The conjecture of Birch and Swinnerton-Dyer for certain elliptic curves with complex multiplication
Ashay Burungale, Matthias Flach
2023-09-06
Number Theory · Mathematics
Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one
R. L. Miller
2011-12-22
Number Theory · Mathematics
The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One
Dimitar Jetchev, Christopher Skinner, Xin Wan
2015-12-23
Number Theory · Mathematics
The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture
Alexander Smith
2025-03-25
Number Theory · Mathematics
Birch and Swinnerton-Dyer conjecture in the complex multiplication case and the congruent number problem
Kazuma Morita
2022-11-30
Number Theory · Mathematics
Elliptic curves with large rank over function fields
Douglas Ulmer
2007-05-23
Number Theory · Mathematics
On the p-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields
Daniel Disegni
2020-10-21
Number Theory · Mathematics
A conditional determination of the average rank of elliptic curves
Daniel Fiorilli
2017-05-17
Number Theory · Mathematics
A divisibility related to the Birch and Swinnerton-Dyer conjecture
Mentzelos Melistas
2022-11-16
Number Theory · Mathematics
Experimental Evidence on a Refined Conjecture of the BSD type
Francisco X. Portillo-Bobadilla
2017-09-06
Number Theory · Mathematics
The Elkies Curve has Rank 28 Subject only to GRH
Zev Klagsbrun, Travis Sherman, James Weigandt
2016-06-24
Number Theory · Mathematics
A classical family of elliptic curves having rank one and the $2$-primary part of their Tate-Shafarevich group non-trivial
Yukako Kezuka, Yongxiong Li
2021-03-12
Number Theory · Mathematics
Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture
Vincent Bosser, Andrea Surroca
2013-01-08
Number Theory · Mathematics
Elliptic curves with all quadratic twists of positive rank
Tim Dokchitser, Vladimir Dokchitser
2013-09-23
Number Theory · Mathematics
Elliptic curves and analogies between number fields and function fields
Douglas Ulmer
2007-05-23
Number Theory · Mathematics
The $p$-parity conjecture for elliptic curves with a $p$-isogeny
Kȩstutis Česnavičius
2014-04-09
General Mathematics · Mathematics
The congruent number problem and the Birch-Swinnerton-Dyer conjecture
Agostino Prástaro
2015-05-05
General Mathematics · Mathematics
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures
Maisara Shoeib
2025-05-27
Number Theory · Mathematics
The Iwasawa Main Conjecture for elliptic curves at odd supersingular primes
Florian Sprung
2016-11-01