# Department of Pure Mathematics and Mathematical Statistics

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 5-descent on elliptic curves
TA Fisher
(2013)
Invariant theory for the elliptic normal quintic, I. Twists of X(5)
T Fisher
– Mathematische Annalen
(2012)
356,
589
Local solubility and height bounds for coverings of elliptic curves
TA Fisher, GF Sills
– Mathematics of Computation
(2012)
81,
1635
Explicit $n$-descent on elliptic curves III. Algorithms
JE Cremona, TA Fisher, C O'Neil, D Simon, M Stoll
– Mathematics of Computation
(2012)
84,
895
The Hessian of a genus one curve
T Fisher
– Proceedings of the London Mathematical Society
(2011)
104,
613
The yoga of the Cassels–Tate pairing
T Fisher, EF Schaefer, M Stoll
– LMS Journal of Computation and Mathematics
(2010)
13,
451
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
JE Cremona, TA Fisher, M Stoll
– Algebra & Number Theory
(2010)
4,
763
Pfaffian presentations of elliptic normal curves
T Fisher
– Transactions of the American Mathematical Society
(2009)
362,
2525
Explicit n-descent on elliptic curves, II. Geometry
JE Cremona, TA Fisher, C O'Neil, D Simon, M Stoll
– Journal für die reine und angewandte Mathematik (Crelles Journal)
(2009)
2009,
63
On the equivalence of binary quartics
JE Cremona, TA Fisher
– Journal of Symbolic Computation
(2009)
44,
673
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