TL;DR
This paper investigates polyquadratic twists of the modular curve X_0(N), providing an algorithm to find twists with local points everywhere, analyzing violations of the Hasse Principle, and exploring reasons behind these violations.
Contribution
It introduces an algorithm for constructing polyquadratic twists of X_0(N) with local points everywhere and analyzes their Hasse Principle violations.
Findings
Algorithm for constructing twists with local points everywhere
Asymptotic estimates for violations of the Hasse Principle
Insights into causes of Hasse Principle violations
Abstract
In this paper, we study the local points of the twist of X_0(N) by a polyquadratic field and give an algorithm to produce such curves which has local points everywhere. Then we investigate violations of the Hasse Principle for these curves and give an asymptotic for the number of such violations. Finally, we study reasons of such violations.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Analytic Number Theory Research