51 citations · 217 across the 26 of their papers we have counts for
5 papers · 1 filter
Minimisation and reduction of 5-coverings of elliptic curves
Tom Fisher
We consider models for genus one curves of degree 5, which arise in explicit 5-descent on elliptic curves. We prove a theorem on the existence of minimal models with the same invar…
Invariant theory for the elliptic normal quintic, I. Twists of X(5)
Tom Fisher
A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant t…
Explicit n-descent on elliptic curves. III. Algorithms
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as curves of degree n in P^{n-1}. The m…
On families of n-congruent elliptic curves
Tom Fisher
We use an invariant-theoretic method to compute certain twists of the modular curves X(n) for n=7,9,11. Searching for rational points on these twists enables us to find non-trivial…
Local solubility and height bounds for coverings of elliptic curves
Tom Fisher, Graham Sills
We study genus one curves that arise as 2-, 3- and 4-coverings of elliptic curves. We describe efficient algorithms for testing local solubility and modify the classical formulae f…