Quadratic Chabauty for modular curves: algorithms and examples

Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings

(2022) Nikola Adžaga et al.   Research in Number Theory

Explicit quadratic Chabauty over number fields

(2021) Jennifer S. Balakrishnan et al.   ISRAEL JOURNAL OF MATHEMATICS

GEOMETRIC QUADRATIC CHABAUTY

(2021) Bas Edixhoven et al.   Journal of the Institute of Mathematics of Jussieu

Quadratic points on modular curves with infinite Mordell–Weil group

(2020) Josha Box   MATHEMATICS OF COMPUTATION

Explicit Coleman integration for curves

(2020) Jennifer S. Balakrishnan et al.   MATHEMATICS OF COMPUTATION

Hyperelliptic parametrizations of $$\pmb {\mathbb {Q}}$$-curves

(2020) Francesc Bars et al.   RAMANUJAN JOURNAL

Quadratic Chabauty for modular curves and modular forms of rank one

(2020) Netan Dogra et al.   MATHEMATISCHE ANNALEN

Explicit arithmetic intersection theory and computation of Néron-Tate heights

(2019) Raymond van Bommel et al.   MATHEMATICS OF COMPUTATION

Modular forms invariant under non-split Cartan subgroups

(2019) Pietro Mercuri et al.   MATHEMATICS OF COMPUTATION

Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties

(2019) Jennifer S Balakrishnan et al.   INTERNATIONAL MATHEMATICS RESEARCH NOTICES

Quadratic Chabauty and rational points, I: $p$ -adic heights

(2018) Jennifer S. Balakrishnan et al.   DUKE MATHEMATICAL JOURNAL

A non-abelian conjecture of Tate–Shafarevich type for hyperbolic curves

(2018) Jennifer S. Balakrishnan et al.   MATHEMATISCHE ANNALEN

Rigorous computation of the endomorphism ring of a Jacobian

(2018) Edgar Costa et al.   MATHEMATICS OF COMPUTATION

Counting points on curves using a map to P 1 , II

(2017) Jan Tuitman   FINITE FIELDS AND THEIR APPLICATIONS

Quadratic Chabauty: p-adic heights and integral points on hyperelliptic curves

(2016) Jennifer S. Balakrishnan et al.   JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK

Computing integral points on hyperelliptic curves using quadratic Chabauty

(2016) Jennifer S. Balakrishnan et al.   MATHEMATICS OF COMPUTATION

Coleman–Gross height pairings and the p-adic sigma function

(2015) Jennifer S. Balakrishnan et al.   JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK

Counting points on curves using a map to $\mathbf {P}^1$

(2015) Jan Tuitman   MATHEMATICS OF COMPUTATION

Tetrahedral elliptic curves and the local-global principle for isogenies

(2014) Barinder Banwait et al.   Algebra & Number Theory

Computing canonical heights using arithmetic intersection theory

(2013) Jan Steffen Müller   MATHEMATICS OF COMPUTATION

Computing Néron–Tate heights of points on hyperelliptic Jacobians

(2012) David Holmes   JOURNAL OF NUMBER THEORY

Massey products for elliptic curves of rank $1$

(2010) Minhyong Kim   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

Appendix and erratum to “Massey products for elliptic curves of rank 1”

(2010) Jennifer S. Balakrishnan et al.   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

The Mordell–Weil sieve: proving non-existence of rational points on curves

(2010) Nils Bruin et al.   LMS Journal of Computation and Mathematics

Minimal resolution of Atkin–Lehner quotients of X0(N)

(2009) Hui Xue   JOURNAL OF NUMBER THEORY

The Unipotent Albanese Map and Selmer Varieties for Curves

(2009) Minhyong Kim   PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES