85 citations · 130 across the 4 of their papers we have counts for
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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…