85 citations · 130 across the 4 of their papers we have counts for
5 papers
Two-cover descent on hyperelliptic curves
Nils Bruin, Michael Stoll
We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In par…
Descent on elliptic curves
Michael Stoll
Let E be an elliptic curve over Q (or, more generally, a number field). Then on the one hand, we have the finitely generated abelian group E(Q), on the other hand, there is the Sha…
Deciding existence of rational points on curves: an experiment
Nils Bruin, Michael Stoll
We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f a squarefree polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For e…
Independence of rational points on twists of a given curve
Michael Stoll
In this paper, we study bounds for the number of rational points on twists C' of a fixed curve C over a number field K, under the condition that the group of K-rational points on t…
An Introduction to Conway's Games and Numbers
Dierk Schleicher, Michael Stoll
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combin…