A database of genus 2 curves over the rational numbers

Andrew R. Booker; Jeroen Sijsling; Andrew V. Sutherland; John Voight,; and Dan Yasaki

arXiv:1602.03715·math.NT·February 20, 2019

A database of genus 2 curves over the rational numbers

Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, John Voight,, and Dan Yasaki

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TL;DR

This paper details the creation of a comprehensive database of genus 2 curves over the rational numbers, including their invariants, Jacobians, and L-functions, integrated into the LMFDB for mathematical research.

Contribution

It introduces a new database of genus 2 curves with detailed invariants, expanding resources available for number theory and algebraic geometry research.

Findings

01

Database includes curves with small discriminant and their invariants.

02

Provides data on Jacobians and associated L-functions.

03

Enhances the LMFDB with genus 2 curve information.

Abstract

We describe the construction of a database of genus 2 curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated L-function. This data has been incorporated into the L-Functions and Modular Forms Database (LMFDB).

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AndrewVSutherland/g2c-data
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