Genus 2 curves with bad reduction at one odd prime

Dabrowski, Andrzej and Sadek, Mohammad (2023) Genus 2 curves with bad reduction at one odd prime. Nagoya Mathematical Journal . ISSN 0027-7630 (Print) 2152-6842 (Online) Published Online First

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The problem of classifying elliptic curves over Q with a given discriminant has received much attention. The analogous problem for genus 2 curves has only been tackled when the absolute discriminant is a power of 2. In this article, we classify genus 2 curves C defined over Q with at least two rational Weierstrass points and whose absolute discriminant is an odd prime. In fact, we show that such a curve C must be isomorphic to a specialization of one of finitely many 1-parameter families of genus 2 curves. In particular, we provide genus 2 analogues to Neumann-Setzer families of elliptic curves over the rationals.
Item Type: Article
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Mohammad Sadek
Date Deposited: 08 Feb 2024 16:00
Last Modified: 08 Feb 2024 16:00

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