** Reader in Number Theory **

*Research Interests: * My research interests are in arithmetical algebraic geometry and computational number theory. In particular I work on elliptic curve descent calculations, and the construction of explicit elements in the Tate-Shafarevich group.

## Publications

The proportion of genus one curves over Q defined by a binary quartic that everywhere locally have a point

– International Journal of Number Theory

(2020)

17,

903

(DOI: 10.1142/s1793042121500147)

Explicit moduli spaces for congruences of elliptic curves

– Mathematische Zeitschrift

(2019)

295,

1337

(DOI: 10.1007/s00209-019-02392-9)

Some minimisation algorithms in arithmetic invariant theory

– Journal de Theorie des Nombres de Bordeaux

(2019)

30,

801

(DOI: 10.5802/jtnb.1050)

On some algebras associated to genus one curves

– Journal of Algebra

(2019)

518,

519

Visibility of 4-covers of elliptic curves

– Research in Number Theory

(2018)

4,

11

(DOI: 10.1007/s40993-018-0106-1)

A formula for the Jacobian of a genus one curve of arbitrary degree

– Algebra and Number Theory

(2018)

12,

2123

(DOI: 10.2140/ant.2018.12.2123)

Computing the Casselsâ€“Tate pairing on 3-isogeny Selmer groups via cubic norm equations

– Acta Arithmetica

(2018)

185,

367

(DOI: 10.4064/aa171108-11-4)

Higher descents on an elliptic curve with a rational 2-torsion point

– Mathematics of Computation

(2017)

86,

2493

(DOI: 10.1090/mcom/3163)

On genus one curves of degree 5 with square-free discriminant

– JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY

(2016)

31,

359

Visualizing elements of order $7$ in the Tateâ€“Shafarevich group of an elliptic curve

– LMS Journal of Computation and Mathematics

(2016)

19,

100

(DOI: 10.1112/s1461157016000243)

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