# Department of Pure Mathematics and Mathematical Statistics

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

Explicit moduli spaces for congruences of elliptic curves
T Fisher
– Mathematische Zeitschrift
(2019)
1
On some algebras associated to genus one curves
T Fisher
– Journal of Algebra
(2019)
518,
519
Some minimisation algorithms in arithmetic invariant theory
T Fisher, L Radicevic
– Journal de Theorie des Nombres de Bordeaux
(2018)
30,
801
Computing the Cassels-Tate pairing on 3-isogeny Selmer groups via cubic norm equations
M van Beek, T Fisher
– Acta Arithmetica
(2018)
185,
367
A formula for the Jacobian of a genus one curve of arbitrary degree
T Fisher
– Algebra & Number Theory
(2018)
12,
2123
Higher descents on an elliptic curve with a rational 2-torsion point
T Fisher
– Mathematics of Computation
(2016)
86,
2493
On genus one curves of degree 5 with square-free discriminant
T Fisher, M Sadek
– JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY
(2016)
31,
359
Visualizing elements of order $7$ in the Tate–Shafarevich group of an elliptic curve
T Fisher
– LMS Journal of Computation and Mathematics
(2016)
19,
100
The proportion of plane cubic curves over Q that everywhere locally have a point
M Bhargava, J Cremona, T Fisher
– International Journal of Number Theory
(2016)
12,
1077
What is the Probability that a Random Integral Quadratic Form in n Variables has an Integral Zero?
M Bhargava, JE Cremona, T Fisher, NG Jones, JP Keating
– International Mathematics Research Notices
(2016)
2016,
3828
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E1.09

01223 764275