** 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

On some algebras associated to genus one curves

– Journal of Algebra

(2019)

518,

519

Some minimisation algorithms in arithmetic invariant theory

– Journal de Theorie des Nombres de Bordeaux

(2018)

30,

801

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)

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

– Algebra & Number Theory

(2018)

12,

2123

(DOI: 10.2140/ant.2018.12.2123)

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

– Mathematics of Computation

(2016)

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)

The proportion of plane cubic curves over Q that everywhere locally have a point

– International Journal of Number Theory

(2016)

12,

1077

(DOI: 10.1142/s1793042116500664)

What is the Probability that a Random Integral Quadratic Form in n Variables has an Integral Zero?

– International Mathematics Research Notices

(2016)

2016,

3828

(DOI: 10.1093/imrn/rnv251)

On families of 9-congruent elliptic curves

– Acta Arithmetica

(2015)

171,

371

(DOI: 10.4064/aa171-4-5)

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