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papers and preprints

The sub-leading coefficient of the L-function of an elliptic curve
Publ. Math. Besançon Algèbre Théorie Lab. Math. Besançon, Besançon, (2016), 95-96.
Preprint or on arxiv or published.

Numerical modular symbols for elliptic curves
Preprint or on arxiv, accepted for publication in Mathematics of Computation (2017).
The code for the computations is available here.

Vanishing of some Galois cohomology groups for elliptic curves
joint with Tyler Lawson
in Elliptic Curves, Modular Forms and Iwasawa Theory edited by David Loeffler and Sarah Livia Zerbes, Springer Proceedings in Mathematics & Statistics, Volume 188, Springer, (2017), 373 - 399
Preprint or on the arxiv or the published version.

Book review: "Fermat's Last Theorem" by T. Saito (two volumes).
Bull. London Math. Soc. (2015) 47 (5): 892-894.
draft or the published version.

A moduli interpretation for the non-split Cartan modular curve
joint with Marusia Rebolledo
Preprint or on the arxiv, (2014).

On the Galois structures of Selmer groups
joint with David Burns and Daniel Macias Castillo.
International Mathematics Research Notices 22 (2015), 11909 - 11933.
Preprint or the published version

On Mordell-Weil groups and congruences between derivatives of twisted Hasse-Weil L-functions
joint with David Burns and Daniel Macias Castillo.
Preprint (2014) accepted in Journal für die reine und angewandte Mathematik
The sage code to compute that was used to compute numerical examples. etnc.py

Overview of some Iwasawa theory
in Iwasawa Theory 2012; State of the Art and Recent Advances edited by Athanasios Bouganis and Otmar Venjakob, Contributions in Mathematical and Computational Sciences, Volume 7, Springer, (2014).
preprint or the published version.

On the integrality of modular symbols and Kato's Euler system for elliptic curves
Documenta Mathematica 19 (2014), 381 - 402.
Preprint or the published version

The class group pairing and p-descent on elliptic curves
joint with Jean Gillibert.
Proceedings of the London Mathematical Society (3) 106 (2013), no. 2, 345–374.
Preprint (pdf) or on the arXiv. The two Sage files class_group_pairing.py and pdescent.py can be used to do numerical computations using the logarithmic class group pairing and isogeny via a p-isogeny.

Algorithms for the Arithmetic of Elliptic Curves using Iwasawa Theory
joint with William Stein.
Mathematics of Computation 82 (2013), 1757-1792.
See here for a preprint version and here for the published version.

Parity conjectures for elliptic curves over global fields of positive characteristic
joint with Fabien Trihan. Compositio Mathemtica, 147 (2011), issue 04, 1105-1128.
Available at compositio or on the arXiv.

Some remarks on self-points on elliptic curves
joint with Christophe Delaunay.
Actes de la Conférence "Fonctions L et Arithmétique", 69-84, Publ. Math. Besançon Algèbre Théorie Nr., Lab. Math. Besançon, Besançon, 2010.
(ps) (pdf)

Self-points on elliptic curves
Algebra and Number Theory 3 (2009), 283-315.
(ps) (pdf)

Self-points on elliptic curves of prime conductor
joint with Christophe Delaunay.
International Journal of Number Theory 5 (2009), 1-22.
(ps) (pdf)

Self-points on an elliptic curve of conductor 14
RIMS Kôlyûroku Bessatsu 4 (2007), 189-195.
(ps) (pdf)

On p-adic elliptic logarithms and p-adic approximation lattices
no longer intended for publication.
(ps) (pdf)

Extending Kato's result to curves with p-isogenies
Mathematical Research Letters 13 (2006), no. 5, p. 713-718
(ps) (pdf)
Tadashi Ochiai found an important error in the paper. The paper "On the integrality of modular symbols ... " contains, among other things, the correction and generalisation of the main result of this paper.

Iwasawa theory of the fine Selmer group
Journal of Algebraic Geometry16 (2007), p. 83-108.
(ps) (pdf)

The fine Tate-Shafarevich group
Mathematical Proceedings of the Cambridge Philosophical Society 142 (2007), no. 1, p. 1-12.
(ps) (pdf) There is further material available on the computations.

On p-adic heights in families of elliptic curves
J. London Math. Soc. (2) 70 (2004) p. 23-40
(ps) (pdf)

Sur la hauteur p-adique dans une famille de courbes elliptiques
Ann. Sci. Math. Québec 28 (2004), no 1-2, 219-223
(ps) (pdf)

Une quintique de genre 1 qui contredit le principe de Hasse
Enseign. Math. (2) 47 (2001), p. 161-172
(ps) (pdf) Errata